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ON THE PROVINCE 



Methods of Teachii^g, 



OE" THE PEOVINOE 



Methods of Teaching. 



A PROFESSIONAL STUDY, 



V BY 

JAMES H. HOOSE, A.M., Ph.D., 

PKINCIPAL OF THE STATE NORMAL AND TRAININO 
SCHOOL, COKTLAND, N. V., 

Author of "Studies in Artieulatioii," "Notes on the Public School 

System of England and Scotland," " Vindication of the Free 

School System" "Practical Suggestiotis to Americans 

Visiting Europe," etc., etc. 



WITH AX LNTRODUCTIOl^ 

BY 

CHARLES W. BENNETT, D.D., 

PROFESSOR OF HISTORY AND LOGIC IN SYBACUSB UNITESSITY. 



1879. .<5^ 



Syracuse, N. Y.: 

DAVIS, BARDEEN & CO., PUBLISHERS. 

NEW YORK : BAKER, PRATT & CO. 

1879. 

9^ 



LBlOZS 



COPTKIGHT, 1879, 
BT 

J. H. HOOSE. 



TO EDUCATORS 

THIS STUDT IS KESPECTrHLIiT 

Bctiicatetf, 

AS A CONTRIBUTION 
TO THE 

PROFESSION OF TEACHING. 



PROFESSIONAL MAXIMS AKD DEFINITIONS. 

" In whatever line of study distinction is sought 
the advantage of good teaching is great." — I. Tod- 
hunter. 

' ' A point which I have incidentally brought for- 
ward deserves some consideration ; I mean the grad- 
ual decay in the educational value of a subject as it 
falls into feebler hands to administer." — Ibid. 

" I am afraid it must be allowed that no art of 
equal importance to mankind, has been so little in- 
vestigated scientifically as the art of teaching." — 
Sir Henry Sumner Maine. 

* ' A good principle not rightly understood may 
prove as hurtful as a bad." — Milton. 

The Investigation of the Principles of Adjusting 
Subject-matter to the Faculties and capabilities of the 
learning Mind — the Process of discovering Methods 
of Teaching — constitutes the conception of the Sci- 
ence of Teaching. (See § 214.) 

The Investigation of Ways of applying Methods of 
Teaching in practice — The Invention of Modes of 
Teaching — is the conception of the Art of Teaching. 
(See § 215.) 

The Investigation of the Science and the Art of 
Teaching constitutes the Profession of Teaching. 
(See § 216.) 



TO THE PEOFESSIONAL STUDENT. 

" The Tlwurjlitful person considers carefully, and 
acts with reflection in regard to the circumstances of 
a case." — C. J. Smith, 

" When I have a case before me, I can't help think- 
ing of it beforehand, and perhaps feeling grieved 
too, afterward, if in any respect I might have con- 
ducted it better. If I am at dinner, the merriment or 
the philosophy of the table-talk suggests something, 
which I put away into a pigeon-hole in my mind for 
the case ; and when I read, be it poetry or prose, the 
case hangs over the page like a magnet, and attracts 
to itself whatever seems to be pertinent or applicable. 
Success or failure leaves a bright or a dark hue on 
my mind, often for days." — Horace Mann, Life, 
p. 74. 

' ' There is a certain reaction against the conserva- 
tism of scientific men at the present time, and the 
imeducated man believes that chance and genius out- 
weigh years of the careful accumulation and sifting 
of facts. . , It is, to say the least, improbable at 
this stage of the world's progress that an ignorant or a 
merely practical man should discover a new force in 
Nature. That dame certainly does not put a pre- 
mium on ignorance." — Tlie Nation, p. 396, No. 704, 
Dec. 26, 1878. 

"Another eiTor is the over early and peremptory 
reduction of knowledge into arts and methods ; from 
which time commonly sciences receive small or no 
augmentation. But as young men, when they knit 
and shape perfectly, do seldom grow to a further 



TO THE PROFESSION'AL STUDEN'T. Vli 

Stature ; so knowledge, while it is in aphorisms and 
observations, it is in growth : but when it once is 
comprehended in exact methods, it may perchance 
be further polished and illustrated and accommo- 
dated for use and practice ; but it increaseth no 
more in bulk and substance. 

" Another error which doth succeed that which we 
last mentioned, is, that after the distribution of par- 
ticular arts and sciences, men have abandoned univer- 
sality, or philosophia "prima : which cannot but cease 
and stop all progression. For no perfect discovery 
can be made upon a flat or level : neither is it possi- 
ble to discover the more remote and deeper parts of 
any science, if you stand but upon the level of the 
same science, and ascend not to a higher science." — 
Bacon, Admncement of Learning, pp. 39, 40, Ed. 
1866. Oxford. 



A LIST OF AUTHORS A^D WORKS QUOTED IN 
THIS VOLUME. 



Jolin W. Armstrong, D.D.— "On Method" (An 
Article). 

Thomas Arnold, D.D. — "Life and Correspondence/' 
by Arthur P. Stanley, M. A, 

" The Art Journal."— Monthly, New York. 

Charles W. Bennett, D.D.—'' History of the Philos- 
ophy of Pedagogics. " 

Alexander Bain, M.A. — Article in " Mind." 

" A Brief English Grammar on a Logical 

Method." 

" Senses and Intellect." 



Francis Bacon. — '• Advancement of Learning." 
Joseph Bosworth, D.D., F.R.S., F.S.A.— "A Com- 
pendious Anglo-Saxon and English Dictionary." 
Wilhelm Adolf Becker. — " Charicles," translated by 

Frederick Metcalfe, M.A. 
Francis Bowen, LL.D. — "A Treatise on Logic; or, 

The Laws of Pure Thought." 
M. Bautain, Professor at the Sorbonne. — "The Art 

of Extempore Speaking." 
Joseph Butler, D.C.L. — " The Analogy of Religion." 
Henry Calderwood, LL.D., F.R.S.E.— "On Teaching : 
Its Ends and Means." 

" Hand- Book of Moral Philosophy." 

Chambers' Encyclopaedia. 
Henry Coppee, A.M. — " Elements of Logic." 
George Crabb, M.A. — " Englisli Synonyms." 
B. F. Cocker, D.D., LL.D.— " The Theistic Concep- 
tion of the World." 
Henry N. Day, LL.D. — " Elements of Logic." 
"Outlines of Ontological Science." 



LIST OF AUTHORS AI^D WORKS. IX 

Davies and Peck — " Dictionary of Mathematics." 

Epictetus — "Discourses translated by George Long." 

English Cyclopedia— Ed. 1867. 

William Fleming, D.D.—" The Vocabulary of Phi- 
losophy." 

Leo H. Grindon — " Life." 

Thomas Henry Huxley, LL.D., F.R.S.— ''Lay Ser- 
mons, Addresses, and Reviews." 

Thomas Hill, LL.D.— " The True Order of Studies." 

Levi Hedge, LL.D. — " Elements of Logick." 

Sir William Hamilton — " Metaphysics." 

W. Stanley Jevons, LL.D., M.A., F.R.S.— Article in 
"Mind." 

" The Principles of Science." 

" Elementary Lessons in Logic." 

William James — Article in " Mind." 

Dionysius Longinus — "On the Sublime," translated 
by William Smith. 

S. S. Laurie, A.M. — "Inaugural Address — Chair of 
Education in University of Edinburgh." 

" Synopsis of Lectures." 

Horace Mann — " Life," by his Wife. 

" Mind " — A Quarterly — London. 

J. D. M. Meiklejohn, M.A. — "Inaugural Address, 
Bell Chair of Education, University of St. 
Andrews." 

J. Clark Murray — " Outlines of Sir William Hamil- 
ton's Philosophy." 

John Stuart Mill — " A System of Logic, Ratiocinative 
and Inductive ; being a Connected View of the 
Principles of Evidence and the Method of Scien- 
tific Investigation." 

Michael Seigneur De Montaigne — " Essays." 

Sir Henry Sumner Maine, R.C.S.Q., LL.D., F.R.S.— 
" Village Communities and Miscellanies." 

L. Mariotti — " Conferences De Pedagogic." 

Henry Longueville Mansel, B.D. — " Metaphysics." 

"Prolegomena Logica." 

James McCosh, LL.D. — "Intuitions of the Mind." 



X LIST OP' AUTHOKS AND WORKS. 

John Ferguson McLennan, M.A., LL.D." — "Primi- 
tive Marriage." 

J, H. Newman, M. A. — "The Idea of A University." 

" The Nation " — A Weekly — New York. 

David P. Page, M.A. — "Theory and Practice of 
Teaching." 

Noah Porter, D.D.— " The Human Intellect." 

Jean Paul Frederick Richter — " Levana." 

Karl Rosenkranz — " The Philosophy of Education, 
or Pedagogics as a System," translated by Anna 
C. Brackett. 

Jean Jacques Rousseau — "Emilius and Sophia," 4 
vols. Ed. 1783. London. 

James E. Thorold Rogers, M.A, — " Education in 
Oxford." 

Laurence Sterne — " Life and Opinions of Tris tram 
Shandy." 

Karl Schmidt — Quoted by Dr. Bennett. 

Henry Sidgwick, M.A.—" The Methods of Ethics." 

C. J. Smith — "Synonyms Discriminated." 

Herbert Spencer — " Education." 

J. A. Stewart — Article in "Mind." 

Sydney Smith — "Essays." 

Louis Soldan — " Method and Manner," in Transac- 
tions of Nat. Ed. Association for 1874. 

James Fitzjames Stephen, Q.C. — "Liberty, Equality, 
Fraternity." 

1. Todhunter, M. A., F.R.S.—" The Conflict of Studies, 
and. other Essays. " 

Edward B. Tylor, LL.D., F.R.S.—" Primitive Cul- 
ture," 2 volumes. 

William Thompson, D.D. — "An Outline of the 
Necessary Laws of Thought." 

Frederick Ueberweg — " System of Logic, and History 
of Logical Doctrines," translated by Thomas M. 
Lindsay, M.A., F.R.S.E. 

Varro — Quoted by Rousseau. 

William Whewell, D.D. — "Novum Organon Reno- 
vatum." 

Richard Whately — " Elements of Logic." 



PREEACE 



The following Study has grown out of one branch 
of the investigations which have occupied my time 
more or less during an extended period of years of 
public labors in teaching. This volume has gradually 
assumed form for my own classes in professional re- 
searches. I have been impressed long with the 
thought that, as teachers and educators of the United 
States, we are too impatient and superficial in our pro- 
fessional inquiries. The consequences are, that our 
theories of teaching rest too heavily upon notions of 
present expediency and brief experience. As a body 
we are in full sjonpathy with the general spirit of the 
nation — we are satisfied with only immediate results. 
Parents urge us to hasten their children into the 
mysteries of learning, for soon they must be placed 
at work, or must enter the advanced schools. The 
legitimate consequences are at our doors : the cry 
of the ujDper schools is, that candidates for admission 
are too poorly prepared for the work in store for 
them ; the experienced men of business complain 
that the youth are not properly grounded in the prin- 
ciples underlying their daily routine of labors ; the 
educated unite in proclaiming the masses uneducated. 
Thus have we been between these upper and nsther 
millstones, crushed and thrown out if immediate 
scholarship was not forthcoming, while we are cen- 
sured in after-years for not having secured more valu- 
able products for the study expended by the children 
in their early school-days. 



Xll PREFACE. 

In this dilemma we have recollected the wisdom of 
the Dutch proverb, " Economy is a great revenue," 
and the German, " Necessity teaches even the lame 
to dance," and the Italian, " Even the dog gets bread 
by wagging his tail," and have endeavored to msure 
to the pupils a scholarship that is frequently too in- 
sufficient to be valuable, but which has secured for 
us an ephemeral reputation and a jeopardized sup- 
port. Under all the circumstances, perhaps we have 
done as well as we could in our schools. 

Because we have yielded so far to the popular de- 
mands, we are to-day without a sharply deiined and 
outlined philosophy in our theories of education and 
of teaching. In our experimentation for sudden 
fruitage we have apparently forgotten that the most 
practical thing in existence is a thoroughly matured 
philosophical theory. Experiments without this 
theory are at random ; they may be successful — 
probably they will not be. Under a correct theory, 
experiments can be tested philosophically, and fail- 
ures reduced to a minimum in number and in degree 
of disaster. In this respect we can learn much from 
those nations that have passed their eager and experi- 
mental age, and are now in their enlightened matur- 
ity. In our ambition to " make scholars," irrespec- 
tive of the elements of necessary time and applica- 
tion, we have overlooked the fact that scholars can 
never be "made;" they must grow: the faculties 
become powers only as time and application enucleate 
them. The active energies of the Profession have 
been too much absorbed in inventing artificial aids, 
helps, short-cuts, and "royal roads" to learning, to 
enter into patient and continued study to discover 
the philosophical nature of the Profession as an Art 
and as a Science. It is time for us to turn our atten- 
tion to find a firmer basis for our practice. This is 
found only in Philosophy. 

" The beginning of philosophy to him at least who 
only enters on it in the right way and by the door, is 



PREFACE. Xlll 

a consciousness of his own weakness and inability 
about necessary things. ' ' — Epictetus. 

The work now submitted is an attempt to outline 
one subject which is included within the conception 
of a complete Philosophy of Education — that of the 
Province of Methods of Teaching. Although the sub- 
ject is not hrst in the order of classification in the 
general investigation of Education, yet because of its 
practical nature it has been directly approached. 

The treatment is somewhat out of the ordinary 
mode of authorship. While I have steadily kept to the 
line of the investigation, yet I have permitted a wide 
range of related matter to incorporate itself into the 
body of the text, even at the- risk of seeming to be 
pedantic. The disadvantages of this apparent hetero- 
geneity are more than compensated by the greater 
suggestiveness of the materials admitted. Besides, he 
who would erect a " liberty-pole" that shall remain 
permanently standing as a beacon must imbed it deep- 
ly into the firmest of soil which the past and present 
have deposited from the attrition of the Ages. 

' ' The reader will please to take it patiently if he find 
what has been already printed again printed here. 
What has been printed is necessary as the bond and 
bast-matting of what has not been printed ; but the 
bast-matting must not cover the whole garden, in- 
stead of merely tying up the trees. But thei'e are 
two still better excuses. Known rules in education 
gain new force if new experience verifies them. The 
author has three times been in the position of trying 
them upon different children of all ages and talents ; 
and he now enjoys with his own the pedagogic j/?/s 
trium liherorum (law of three children) ; and every 
other person's experience related in this book has been 
made his own. Secondly, printing-ink now is like 
sympathetic ink, it becomes as quickly invisible as 
visible ; wherefore it is good to repeat old thoughts 
in the newest books, because the old works in which 
they stand are not read. Kew translations of many 
truths, as of foreign standard works, must be given 



XIV PREFACE. 

forth every half century. And, indeed, I wish that 
even old German standard books were turned into 
new German from time to time, and so could find 
their way into the circulating libraries. 

" Why are there flower and weed gleanings of 
every thing, but no wine or corn gleanings of the in- 
numerable works on education ? Why should one 
single good observation or rule be lost because it is 
imprisoned in some monstrous folio, or blown away 
in some single sheet ? For dwarfs and giants, even 
in books, do not live long. Our age, this baUoon, or 
air-ship, which, by simultaneous lighting of new 
lamps, and throwing out of old ballast, has constantly 
mounted higher and higher, might now, I should 
think, cease to throw out, and rather lovingly en- 
deavor to collect than to disperse the old. 

"However little so disjointed a collection of 
thoughts could teach rules, it would yet arouse and 
sharpen the educational sense, from which they orig- 
inally sprung 

* * Something very different from such a progressive 
cabinet of noble thoughts, or even from my weak 
Lemma, with her fragments in her arms, is the usual 
kind of complete system of education which one 
person after another has written, and will write. 
It is difficult, — I mean the end, not the means. 
For it is very easy to proceed with book-binder's and 
bookmaker's paste, and fasten together a thousand 
selected thoughts with five of your own, especially if 
you conscientiously remark in the Preface that you 
have availed yourself of the labors of your predeces- 
sors, yet make no mention of one in the work itself, 
but sell such a miniature library in one volume to 
the reader as a mental facsimile of yourself. How 
much better in this case were a hole-maker than a 
hole-hider ! How much better were it if associated 
authors (I mean those friendly hundreds who move 
along one path, uttering precisely the same sound) 
entirely died out — as ' Humboldt tells us that in the 
tropical regions there are none of those sociable 



PKEFACE. XV 

plants which mnke our forests monotonous, but next 
each tree a perfectly different one grows. A diary 
about an ordinary child would be much better than 
a book upon children by an ordinary writer. Yes, 
every man's opinion about education would be valu- 
able if he only wrote what he did not copy. The 
author, unlike a partner, should always only say 
'I,' and no other word." — Jean Paul Richter, 
Levana, Author's Preface, pp. xii-xv, ed. 1863. 

Although Methods of Teaching occupied the atten- 
tion of some of the Greek philosophers, and have con- 
tinued before the minds of educators in portions of 
Europe down to the present date, and have of late 
engaged thought in the United States, yet they have 
been confounded generally with Methods of Educa- 
tion, Modes and Manners of Teaching, rather than 
apprehended as constituting a province by them- 
selves. The subject of the inquiry being 'intricate 
in its character, it has been no easy task to elaborate 
it. I have diligently sought nothing but Truth. 
Should subsequent researches, observations, or ex- 
perience, from whatever source, reveal aught of error 
in the positions advanced, no one shall outdo the 
author in haste to accept the facts as they shall ap- 
pear. If this investigation, with all of its imperfec- 
tions of style, matter, and treatment, shall prove as 
interesting to the Fraternity as it has to the writer, 
it will serve its purpose. "Indeed, its largeness, 
its infinity, embarrass me. It is like an attempt to 
lift the earth : the arms are too short to get hold of it. 
However, I hope to get hold of a few handfuls." 
Horace Mann, Life, p. 87, Boston, 1865. 

** I have long known that no man can apply himself 
to any worthy subject, either of thought or action, 
but he will forthwith find it develop into dimensions 
and qualities of which before he had no conception. 
If this be true of all subjects worthy of rational at- 
tention, how extensively true is it of the all-compre- 
hending subject of education ! This expansion of 
any object to which our attention is systematically 



XVI PREFACE. 

directed may be compared to the opening of a con- 
tinent upon the eye of an approaching mariner. At 
first he descries some minute point, just emerging in 
*he distance, — the lofty summit of some mountain. 
As he approaches, other elevated points seem to rise 
out of nothing, and stand upon the horizon ; then 
they are perceived to be connected together ; then 
hills, cities, towns, plains, rivers, which the eye can- 
not count for their numbers, nor embrace for their 
distance, fill up the admiring vision. So it is in ap- 
proaching any of the intellectual or moral systems 
which Nature has established. "—iJid , pp. 84, 85. 

J. H. H. 
State Normal and Training School, 
Cortland, N. Y., Jan. 1, 1879. 



ANALYTICAL TABLE OF CONTENTS. 



PAGE 

Dedication iii 

Professional Maxims v 

To THE Professional Student vi-vii 

A List of Authors and "Works Quoted viii-x 

Preface xi-xvi 

Table of Contents xvii-xxx 

Introduction— By Dr. Charles W. Bennett xxxi-xxxvii 



ANALYTICAL TABLE OF CONTENTS. 



PART FIRST. 

Introductory Discttssion — On Pedagogics, Education, 
Teaching, Authorities 

I. On Pedagogics. 

SECTION PAGE 

1. Pedagogics— definition of From Soldan 3 

2. Pedagogics— definition of From Rosenkranz 4 

3. Pedagogics— definition of From Schmidt, quoted by 

Bennett 4 

II. On Education. 

4. Education— province of 5 

5. Education— province of From Rousseau 5 

6. Education— province of From Rosenkranz 6 

7. Education— province of From Rogers 9 

8. Education— province of From Bain 9 

9. Education— province of From Je vons 20 

10. Education— province of From Varro 23 

11. Education and Training From Smith 22 

12. Education — province of From Hill 23 

13. Education— province of From Page 24 

14. Education— province of From Huxley 26 

15. Education— province of From Laurie 30 

10. Education— province of From Richter 34 

17. Education vs. Instruction From Richter 42 

18. Education vs. Teaching 43 

19. Education vs. Teaching From Caldervvood 43 



Ai^ALTTICAL TABLE OF CONTEi^TS. XIX 
in. On Teaching. 

SECTION PAGE 

20. Language— represents 44 

21. Teaching— meaning of From the Greek 45 

22. Teaching— meaning of From the Latin 47 

23. Teaching— meaning of From the Anglo-Saxon 49 

24. Methods of Teaching— expression determined 50 

25. Authority in Anglo-Saxon Conception of Teaching- 

illustrated From Todhunter 51 

26. Same idea— illustrated From Jevons 51 

27. Same idea— illustrated From Calderwood 53 

28. Conception of Teacher limited to Persons 54 

29. Teach, Instruct, Inform— defined From Crabb 55 

30. Teach, Instruct, Inform— defined From Smith 57 

IV. On Authorities. 

31. Authority— defined From Crabb 60 

32. Authority— defined From Smith 60 

33. Authoritj', Consent, Assent, Belief — defined. 

From Fleming 61 

34. Authority— general discussion From Bacon 69 



.V. Recapitulation 77 



PART SECOND. 

On Method in General. 

36. Method— defined ' 79 

37. Method— refers to subject-matter 80 

38. Methods of Business— customary use of Expression 80 

39. Methods of Business— illustrated. .From " The Nation " 81 

40. Three distinct Elements in an Investigation— (1) Object- 

matter, the end ; (2) Way in which faculties pro- 
ceed ; (3) State of Investigator 82 

41. I. Object-matter of Study— considered— ends in ySV-^^em. 83 

42. II. Ways of Procedure of Mind— considered— Are modes 

of method , 85 

43. (a) A7ialysis—de&ned 85 



XX ANALYTICAL TABLE OF COKTEl^TS. 

SECTIOK PAGE 

44. Analysis VS. Separation 86 

45. {b) Synthesis— de&iuid 87 

46. Synthesis and Definition 87 

47. Abst7'action— defined 87 

48. Analysis and Synthesis are parts of same Method. 

From Hamilton 87 

49. Synthesis vs. Reconstruction 88 

50. (c) Generalization— denned 89 

51. id) Classification— defined 89 

52. ie) Induction— denned 90 

53. Induction vs. Intejw^tation 90 

54. Induction vs. Repetition 92 

55. if ) Deduction— denned 93 

56. III. State, or Ways of Investigator— give rise to Manned'. 93 

57. Manner Systematized is Mode 94 



PART THIRD. 

I, On the Theory of Methods of Teaching. 

58. Introduction— Need of Better Methods From Maine 96 

59, Theory of Methods of Teaching— hased upon Psychology 

and nature of subject-matter 98 

CO. Nature of Faculty— defined 98 

61. Character of Faculty— defined. . . 98 

62. Psychology— defined 98 

63. Psychology— province of. From Stewart 98 

64. Objects and Limitations of Present Investigation 101 

65. Knowing— forms of knowledge From Ueberweg 103 

66. Form and Matter From Thompson 103 

67. Form and Matter From Jevons 105 

68. Form and Matter From McCosh 105 

69. Form and Matter From Newman 107 

70. Form of Matter— (a) Illustrated.. .From "The Nation" 

(6) Illustrated From Rousseau 107 

71. Knowledge, Learning, Erudition— defined. .From Crabb 108 



ANALYTICAL TABLE OF COKTEiq^TS. XXI 

SECTION PAGE 

72. Knowledge— defined. . From Day 110 

73. Knowledge— defined From Day 111 

74. Knowledge— aim of, is truth From Ueberweg 112 

75. Knowledge— stages of, in acquiring : (1) Source of— re- 

sides in mind ; (2) Rational way of procedm-e is 
under Will ; (3) End of activity is Knowledge 113 

76. Teaching— defined 114 

77. Self-Informed is Self-educated— defined and amplified. . . 114 

78. Teachers are a Necessity to Learners— Teacher, what is 

—Adjust, defined From Smith 115 

79. Teaching— defined 116 

80. Teacher— duties of, to analyze and separate subject- 

matter in 

81. Teacher— duty to note both form and matter of knowl- 

edge in mind of learner 117 

82. How to Teach ?— is great question 118 

83. Teaching— Conception of, requires examination of : (1) 

Mind of learner— learner ; (2) Mind of teacher- 
teacher ; (3) Things to be learned— subject-matter.. 118 

84. Teaching— Conception of, resolves itself into: (1) Teacher 

must know subject-matter ; (2) Teacher must know- 
mind ; (3) Teacher must know Way in which mind 
proceeds when learning— Constitute Profession of 
Teaching 119 

85. Recapitulation of §§82, 83 120 

86. Province of Methods op Teaching— that of Princi- 

ples of Adaptation of Subject-matter to Faculties of 
Mind 121 

87. Principle— defined From Fleming 122 

88. Principle— defined. . From Smith 122 

89. Methods of Teaching— require system of subject-matter. 123 

90. Systems and Methods— compared 123 

91. Province of Methods of Teaching, not that of Pedagogics 

or Ethology 125 

92. Ethics— defined ^ From Sidgwick 125 

93. Teaching is Handmaid of Education 126 

94. Methods of Pedagogics, Scope of— equivalent to Meth- 

ods of Education 127 



XXll ANALYTICAL TABLE OF COKTEl^TS. 

SECTION PAGE 

95. Methodick of Education— defined. (1) Educator must be 
a Guide— Processes : Analytic, Syutlietic, Inductive. 
(2) Educator must guide Morals— Methodick of Edu- 
cation is Methodology, Way, Procedure— Method- 
ick— rests on the Will. Departments of— particu- 
lar methods From Laurie 129 

G6. Methods of Education regard Growth of Mind as an 
End— They consider : (1) What Subjects to be 
Taught— purpose of. (2) How to Instruct for Right 
Judgments. Answers : To (1) Doctrine of the Real— 
To (2) Formal Discipline From Laurie 131 

97. Grow^th and Development— contrasted... From Spencer 132 
Growth— defined From Smith 132 

98. Methods of Teaching regard Growth of Mind as a Means 13^ 

99. Methods of Teaching Examined in their Relation to 

" IIow to Study " 136 

100. Methods of Teaching do not distinguish between Truth 

and Error of Subject-matter taught 138 

101. Methods of Teaching assume innate Activity of Mind- 

Examined in relation to " Waking up Mind"— Con- 
ception of " Variety" examined 1.39 

102. Attention— defined and examined From Richter 139 

103. Excite, Awaken, Rouse, Incite, Stimulate— defined. 

From Smith 141 

104. Methods of Teaching— not responsible for Form of 

Knowledge in Mind of Learner 142 

10.5. " Development of Ideas"— analyzed 144 

106. Thorough Teaching— defined 144 

107. Develop, Unfold, Unravel— defined From Smith 145 

108. Methods of Teaching must regard Procedure of Facul- 

ties when learning 148 

109. Methods of Discovery and of Instruction. From Jevuns 149 

110. Methods of Teaching must respect Inherited "Cast of 

Mind " 160 

111. Methods of Teaching— difficult to suit, because of evan- 

escence of psychological phenomena 163 

112. Methods of Teaching— in present state of Psychology, 

not absolutely invariable 163 



AN'ALYTICAL TABLE OF CONTENTS. Xxiii 



SECTION PAGE 

13. Methods of Teaching examined in relation to "Class- 
Drill" 164 

114. Methods of Teaching do not regard Individuality of 

Teacher Kj^ 

115. Manner— Examined and defined 165 

116. Teacher can have "His Manner," not "His Method". 166 

117. Methods of Teaching— are not method in general 166 

118. Method and Manner— contrasted From Soldau 167 

119. Mode of Teaching— defined 168 

120. Methods, Modes, Mannei's— compared 168 

121. In Perfect Knowledge, all Teachers would Teach alike 

in their Modes 169 

122. Methods of Teaching — Misconception of occasions Mis- 

use of the Expression 170 

123. Mode, Manner— defined From Smith 

Mode, Manner— used From " The Nation" 171 

124. System, Method— defined From Smith 

System— defined From Jevons 172 

125. Method, Procedure— defined From Mariotti 172 

126. Method, Mode— defined From Armstrong 173 

127. Principle, Law, Rule— defined From Armstrong 173 

128. Method, Mode, Manner— difference, (a) Elustrated by 

Figure of a Bridge ; (6) Illustrated by Water as 
buoying-up power ; (c) Illustrated by Gravity, Ani- 
mal Power, Steam ; (ff) Illustrated by Horse Power, 
Carriage, Landau 174 

129. Mode— properly used From Page 175 

130. Mode of Teaching— illustrated From Page 175 

131. Method— improperly used From Rousseau 176 

132. Method— Socratic Mode— illustrated. . .From Epictetus 178 

133. Methods of Teaching— for Modes and Manners— Cri- 

tique upon From Meiklejohn 184 

134. "Methods of Nature"— Conception of, Examined— 

Hlustration From Rousseau 

Illustration From McLennan 188 

135. Artificial— Conception of, examined 190 

136. Natural, in general, is not Natural in the Individual 192 

137. Natural— defined From Butler 193 



XXIV ANALYTICAL TABLE OF COKTEKTS. 

SECTION PAGE 

138. Nature— defined From Cocker 193 

139. Nature— Law of— defined From Cocker 194 . 

140. Nature— Universality of Order of— defined— not Inva- 

riable From Cocker 194 

141. Nature— defined From Fleming 196 

142. Natural— Instance of From Epictetus 200 

143. Natural and Artificial Education— discriminated. 

From Huxley 202 
n. On the Practice of Methods of Teaching. 
(A) On the Knowing Faculties of the Mind. 

144. Purpose of this Division is to submit a Basis for Meth- 

ods of Teaching 203 

145. Psychological Phenomena— classified. (1) Phenomena 

of Cognitions ; (2) Phenomena of Feelings ; (3) Phe- 
nomena of Conations From Hamilton 204 

146. Consciousness— defined. Involves : (1) A Knowing Sub- 

ject, the Ego ; (2) A Recognized Modification of 
Ego ; (3) A Recognition by the Subject of the Modi- 
fication (a) From Hamilton 

(6) From James 204 

147. I. Presentative Faculties From Hamilton 205 

148. ll. Memory— Faculty of From Hamilton 207 

149. III. Reproductive Faculty From Hamilton 207 

150. rV. Imagination From Hamilton 208 

151. V. Elaborative Faculty From Hamilton 208 

152. VI. Regulative Faculty From Hamilton 209 

153. Recapitulation of Cognitive Faculties. .From Hamilton 210 

154. Will, the Principal Faculty in acquiring Knowledge. 

From Richter 211 

155. Will— same idea From Laurie 213 

156. Will— same idea From Cocker 213 

157. Imagination— (a) The Poetic From Porter 214 

158. Imagination— (^>) The Philosophic From Porter 214 

159. Imagination— (c) The Ethical Uses of From Porter 216 

160. Imagination— (c^) Relation to Religious Faith. 

From Porter 217 

161. Imagination is Over-developed in the Youth of India. 

From Maine 218 



ANALYTICAL TABLE OF CONTEIffTS. XXV 

SECTION PAGE 

1G2. Memory— Modification— defined 219 

163. Memory— Active— Childhood need not Understand all 

it Learns From Arnold 219 

164. Memory, Imagination, and Hope are the same Faculty. 

From Mansel 220 

165. Memory— Permanence of From Grindon 221 

166. Memory— Limited in its Growth From Eichter 224 

167. Memory— Retains best from Contrasts... From Richter 220 

168. Memory— a Goddess From Montaigne 227 

169. Memory— a Personal Reminiscence. . . .From Montaigne 227 

170. Memory and " Cram" From Maine 235 

171. Memory and " Cram" From Todhunter 240 

172. Memory and "Cram," and Thinking Faculties— A 

Question-Begging Epithet ; Analysis of "Cram;" 
"Good Cram" and -'Bad Cram" defined ; Dulness 
and 'Cram ;" Book-work and " Cram ; " Exami- 
nations are Tests ; Repetition in Teaching Neces- 
sary ; Purpose of "Good Cramming;" Intense 
"Cramming" is Real Education; Remarks of 
Home-Secretary Ci OSS ; Mr. Cross Answered ; Slow 
and Deliberate Teaching compared with Rapid; 
Object of School ; Purpose of Liberal Education ; 
Not Desirable to Remember things Taught in 
School; Source of Error not in Memory, but in 
Distinguishing between Form and Matter; Reten- 
tion ; Barristers must Forget ; Work of Teachers 
not to make Philosophers, and Scholars, and Ge- 
niuses—these are Born ; Business of Educator is 
" to Cram" From Jevons 241 

173. Knowing, Act of— defined From Ueberwcg 257 

174. Knowledge— defined From Ueberweg 258 

175. Human Thought— determined From Ueberweg 258 

176. Knowledge— Activity necessary to From Ueberweg 258 

177. Knowledge— defined From Calderwood 259 

178. Thought— Difference between, and other Phenomena 

of Mind — Intuition, Conception, Concept, Con- 
sciousness, Representation, Perception, Imagina- 
tion From Mansel 259 



XXVI Aiq'ALYTICAL TABLE OF CONTEl^TS. 

SECTION PAGE 

179. Thought— defined From Mansel 265 

180. Thought— Faculty of— defined— Judgment •, Apprehen- 

sion ; Conception is a Psychological Judgment ; 
Conceiving ; Language is a sign of Intuitions ; Ab- 
straction; Concept; Common Language and Com- 
mon Thought ; Identity ; Reasoning defined ; Syl- 
logism ; Recapitulation From Mansel 266 

181. Powers— Mental, employed in acquiring Knowledge- 

Discrimination; Power of Detecting Identity; Power 

of Retention From Jevons 274 

183. Identity and Difl'erence— Laws of. (1) Law of Identity; 
(2) Law of Contradiction ; (3) Law of Duality. 

From Jevons 277 

183. Thought— First Gradation of, is the Formation of Judg- 

ment — Proposition ; Sentence ; Concept ; Conceiv- 
ing ; Reasoning ; Perception ; Regulative Faculty, 
or Faculty of Intuition ; Being; Existence; Matter 
of Thought ; Analysis ; Abstraction ; Attention ; 
Comparison; Synthesis; Subject; Predicate; Terms 
of a Proposition ; Copula From Day 279 

184. Thought— Second Gradation of, is the Formation of 

Co/?c-f/;f— Judgments ; Forming Concepts ; Terms ; 
Concept in Comprehension ; Conception ; Faculty; 
Act ; Product ; Law of Identity ; Base ; Relative 
Cognition ; Concepts differ from Judgments ; Con- 
cept not Expressed ; Concept implies Judgments ; 
Base of Concept ; Concepts are Products of Thought; 
Thought aggregated by single Words From Day 288 

185. Thought— Third Gradation of, is Beasoning—B.Qdi&wv- 

ing derived from Judgment ; Reasoning not a Con- 
clusion ; Reasoning defined ; Ratiocination ; Dis- 
course ; Discursive ; Argumentation ; Inference 
or Illation ; Conclusion ; Syllogism ; Parts of Rea- 
soning ; Antecedent ; Consequent ; Immediate Rea- 
soning ; Mediate Reasoning From Day 296 

186. Reason— has no Relation to Body From Griudon 301 

187. Thinking is Conversation of Soul with itself. 

From Mansel 301 



AITALYTICAL TABLE OF COKTEKTS. XXVll 
(B) On the Nature of Subject-Matter. 

SECTION PAGE 

188. Methods of Teaching— Tccaclier to discover, must know 

Mind and Nature of Subject-matter 303 

189. Subject-matter— defined 302 

190. Subject-matter— Material— Exists outside of Miud 302 

191. Subject-matter— Immaterial— Created wholly by Mind . 302 

192. Object Teaching— Conception of, Analyzed 303 

193. Object Teaching— when Valuable 304 

194. Object Teaching— when Possible 304 

195. Illustrative Teaching— defined 304 

196. Ideas— Succeed each other according to Laws of Asso- 

ciation 305 

197. Illustrations— defined, by Illustrations— defin- 
ed From Smith 

Analogy— defined From Smith 

Analogy and Induction— Difi:"erence From Fleming 305 

198. Illustrations— Example of From Sterne 306 

199. Illustrative Teaching— Analogous Extension of Mean- 

ing of "Words From Jevons 309 

200. Illustration— differs from Example 309 

201. Illustrative Teaching is Objective Teaching 309 

202. Illustrative Teaching — Conception of, misunderstood 

for Object Teaching, has occasioned abuse of the 
Expression 310 

203. Mathematics— cannot be taught by Object Teaching- 

only Illustratively 310 

204. Mathematics— Nature of Arithmetical Numbers . 

From Jevons 
Number— defined From Davies and Peck 312 

205. Mathematical Judgments— on Nature of. .FromMansel 314 

206. Mathematical Judgments— on Arithmetic, Geometry. 

From Eng. Cycl. 324 
20'7. Mathematical Judgments— on Numeration. 

From Whewell 326 

208. Object Teaching— Branches that can be Taught in this 

way 327 

209. Objects — when their Value ceases in Teaching and 

Learning 328 

210. ObjectTeaching— must be succeeded by Thought 329 



XXVlll AKALTTICAL TABLE OF CONTENTS. 

(C) On Discovering Methods of Teaching Special Svhjects. 

SECTION PAGE 

211. System of Subject-matter must be constructed by 

Teacher— Principle of Adaptation must be Discov- 
ered for Method of Teaching , 330 

212. Addition— on Discovering the Method of Teaching it. . . 331 

(1) On the Nature of the Subject-matter 331 

(2) On the Faculties primarily active in Learning Ad- 

dition 332 

(3) On Inventing the Mode of Teaching Addition 333 

213. Mode and Manner of Teaching Addition— liecapitu- 

lated 333 

214. Science op Teaching— defined 334 

215. Art of Teaching— defined 334 

216. Trofession of Teaching— defined 334 

ni. Concluding Reflections. 

217. To Teach— Qualifications Eequisite 335 

218. Growth— Evil effects of missing Opportunities for. 

From Meiklejohn 335 

219. Teacher— Should be a Learner From Arnold 336 

220. Teacher— Value of Common-Sense From Sidgwick 338 

221. Teacher— Value of Common-Sense for.. From Whately 339 

222. Teacher— Best Talent for, is Judging Right upon Im- 

perfect Materials From Stephen 344 

223. Difference between Theory and Practice— of Degree 

only, not of Kind . .From Mansel 344 

224. Science of Human Nature— Possible From Mill 344 



APPENDIX OF QUOTATIONS. 



SECTION PAGE 

225. A.— On Method. 

1. FromHedge 346 

2. From Coppee 347 

3. From Day 348 

4. From Fleming 350 

5. From Bain 356 

6. FromWhewell 357 

7. FromBowen 361 

8. From Day 368 

9. FromComte 373 

226. B.— On System. 

1. From Fleming 376 

227. C— On Analysis. 

1. From Fleming 380 

228. D.— On Synthesis. 

1. From Fleming 383 

229. E.— On Definition. 

1. From Fleming 385 

2. From Mill 389 

230. F.— On ABSTRA.CTION. 

1. From Fleming 390 

231. G.— On Genekalization. 

1. From Fleming 392 

2. FromJevons 395 

232. H.— On Classification. 

1. From Fleming 398 

2. From Jevons 401 

233. I.— On Induction. 

1. From Smith 413 

2. From Day 415 



XXX APPENDIX OF QUOTATIOi^^S. 

SECTION PAGE 

3. From Fleming 416 

4. From Whewell 422 

5. From Eng, Cyclop 423 

6. From Jevons 434 

7. From Mill 451 

234. J.— On Interpretation. 

1. From Davies and Peck 473 

2. From Smith 477 

235. K.— On Deduction, 

1. From Fleming 478 

2. FromDay 480 

3. From Bo wen 482 

4. From Hedge 484 



INTRODUCTION. 

BY 

CHARLES W. BENNETT, D.D. 



USTTRODUCTIOE". 



The subject of education is each year assum- 
ing growing prominence. It cannot be justly 
charged that the Eastern, Middle, and Western 
States of the American Union have been indiifer- 
ent to the claims of their citizens to enjoy op- 
portunities of instruction and enlightenment. 
Nearly all of them have made generous provi- 
sions for primary and intermediate instruction, 
and in some have been elaborated complete sys- 
tems of education from lowest to highest. 

Nor has the question of Training Schools for 
teachers been neglected. Good general educa- 
tion presupposes good schools, and good schools 
presupposes good teachers ; hence that State 
which fails to provide for good teachers exhibits 
a plain lack of practical wisdom. These Nor- 
mal or Training Schools have been subjected to 
severe criticism, both as to the scope and charac- 
ter of their work, as well as the products which 
they have yielded to the State. Many able 
thinkers have believed that the nature and prov- 
ince of the instruction in these State schools 
was not sufficiently definitive to warrant their 
independent existence and exceptional support ; 



xxxiv i:n'tkoductiok. 

tliat the Common Schools, Academies, and Sem- 
inaries of the State were doing essentially all 
which was accomplished by the expensive ma- 
chinery of Normal Schools ; that the conception 
of the use and desio-n of Teachers' Trainino; 
Schools, as entertained by those who had inaug- 
urated and managed them, was essentii-lly erro- 
neous ; that they had failed to elevate teaching 
to the dignity, honor, and emoluments of a pro- 
fession ; that a large fraction of those who had 
been thus educated chiefly at the public expense 
had not rendered to the State adequate remun- 
eration in superior service and skilled labor. 
Doubtless some of the writing and sjDeaking on 
this subject has been hypercritical ; since the 
difficulties of the educational problem have not 
been sufficiently appreciated, and the amount 
and quality of the hard work done by those who 
have had charge of these Training Schools have 
not been properly recognized. Nevertheless, 
that the expectations of the best friends of edu- 
cation have not been fully satisfied must be 
frankly acknowledged. Too much time and en- 
ergy have been consumed in the mere prelimin- 
aries to strictly Training Schools. The require- 
ments for admission have been too low. The 
three great departments of Psychology, History 
of Pedagogics, and Methodology and Training, 
which should occupy by far the largest portion 
of the course of study, have been in too many 
instances but meagrely examined, and in most 
of these schools the historical examination has 
scarcely been touched upon at all. 



INTRODUCTION^. XXXV 

We, therefore, -welcome the present work of 
Dr. Hoose as a promise that a better day for 
Normal School Training is dawning. It shows 
that at least one Chief in these Schools is fully 
awake to the necessity of careful and exact 
thinking on one of the few subjects of study 
which legitimately belong to Training Schools. 
The importance of the branch of education here 
treated can hardly be over-emphasized. Lack 
of clearness here brings obscurity and partial 
failure into the whole career of the teacher. He 
may, by long experimentation with mind, cor- 
rect some mistakes ; but unless the principle 
which underlies Method is fully understood in 
the outset, it is difficult to compute the mischief 
which may ensue. 

The work which is here presented professes to 
reveal and discuss this principle. As stated in 
his preface, during the ten years of his supervi- 
sion of one of the largest Training Schools of 
New York, the author has been continually study- 
ing, and yearly developing this subject before the 
classes which have been under his tuition. Like 
most valuable products it has, therefore, been a 
growth from the experience and close observa- 
tion of an eminently practical teacher. This 
should greatly enhance its value. In the direct- 
ness, brevity, and pertinence of statement and il- 
lustration, the author seems to have the wants 
of his classes ever distinctly before him. Evi- 
dently he is no recluse thinker, but a busy man 
among busy men and women who need his help, 
and whom he wants to help. 



XXXVl INTRODUCTIOK. 

The extended quotations from so many emi- 
nent thinkers and educators may, in the opinion 
of some, smack a little of pedantry. But since 
one great object of such a work is to stimulate 
to further research, as well as to instruct the un- 
initiated, these references to and quotations 
from the works of philosophic thinkers must be 
r(5garded not only pertinent, but invaluable. 
Moreover, the assumption of originality may be 
cheap with those of slender information, but the 
real student becomes quite content at times to 
sit at the feet of those giants who have wrestled 
with the hard problems of education, and endeav- 
or to reduce their thoughts to practical and effi- 
cient uses. He usually does most for his pupils 
and readers who opens up to them the literature 
of his subject, and directs them to the sources of 
his own inspiration and quickening. The teacher 
in Training Schools especially must ever consider 
that lie is dealing with minds of greater or less 
maturity, who are, with himself, desirous to go 
to the fountain-heads of knowledge and truth, 
and there drink for themselves. While this 
course of procedure may prove terribly iconoclas- 
tic to those who may be worshipping the false 
idol of originality, it will always be most help- 
ful to the real lover of truth, and become most 
beneficent to our fellow-workers. 

It is highly probable that some positions of the 
author will not pass unchallenged. Some read- 
ers may be inclined to believe that his boldness 
sometimes verges on rashness, and that in some 
points he has not fully established what he 



IKTEODUCTIOiq-. XXXYll 

claims : but in all tlie work tliere breathes the 
spirit of lion est conviction ; and honest thinking 
cannot long remain wrong thinking after the 
wrong has been pointed out. If by frank and 
generous criticism it shall be shown that the au- 
thor has inadvertently been led to make any mis- 
statements of fact or principle, these corrections 
will probably be thankfully received, and can be 
easily incorporated into the text of some future 
edition. 

The subject here presented by Dr. Hoose is 
specially worthy of investigation and attention 
on the part of the directors of Training Schools ; 
indeed, none are of greater value. Hence we 
must believe that this work will be cordially wel- 
comed by the teachers of Normal Schools, by 
the graduating classes of these schools, and by 
all thorough teachers, as supplying a long-felt 
need. 

CHAS. W. BENNETT. 
Sybacuse University, January 1, 187U. 



PART FIRST. 

§§ 1-35. 

INTRODUCTOEY DISCUSSION. 



I. On Pedagogics, . . . . § § 1-3. 

II. On Education, . . . • § § 4^19. 

III. On Teaching, ... § § 30-30. 

IV. On Authorities, , . . § § 31-34. 

V. Recapitulation, .... § 35. 



I. 

ON PEDAGOGICS. 

1. ** By Pedagogics we mean the science of 
the reaUzation of the human rational potentiality 
into actuality. In the human mind lie certain 
capabilities which do not manifest themselves 
unless drawn out by external influence or an 
inherent principle of development. Although 
there be no development of these faculties, they 
may still exist, but are not manifest. They re- 
main in a dormant or latent state, they exist as 
possibilities, or in potentia. By an educating 
or developing influence these latent capabilities 
become manifest, and from the state of potenti- 
ality pass over to the state of actuality. To use 
an illustration, we may say that the seed makes 
the growth of the plant possible : it contains the 
possibility of the plant. Hence, to express the 
same thought in a different way : The seed is the 
potentiality of the plant ; sun and soil will trans- 
form this potentiality into actuality, the plant it- 
self. All actual, finite existence must have passed . 
through the stage of potential existence. Peda- 
gogics is the science of the transition of man 
from his natural potentiality to actuality."^ 
[Proceedings of the National Educational Asso- 



4 OK PEDAGOGICS. 

elation, 18*74, p. 246. Paper by Prof. Louis 
Soldan.) 

2. " Pedagogics as a science must (1) unfold 
the general idea of Education ; (2) must exhibit 
the particular phases into which the general work 
of Education divides itself, and (3) must describe 
the particular standpoint upon which the general 
idea realizes itself, or should become real in its 
special processes at any particular time. 

It busies itself with developing a priori the idea 
of Education in the universality and necessity of 
that idea. . . . Pedao^oofics as an art is the 
concrete individualizing of this abstract idea in 
any given case. . . . The idea of Pedagog- 
ics in general must distinguish, (1) The nature 
of Education in general ; (2) Its form ; (3) Its 
limits." (Rosenkranz, Pedagogics as a System, 
pp. 7-9, ed. 1873. Translated by Anna C. 
Brackett. ) 

3. "Pedagogics is the science and art of so 
developing, by means of conscious influence on 
the physical, intellectual, and moral powers of 
man, the ideas of truth, freedom, and love, that 
lie at the foundation of his God-derived nature, 
that he can meet spontaneously, and indepen- 
dently, his human responsibilities. ' ' (Schmidt, 
Geschichte der Erziehung, p. 1, quoted by Dr. 

•C. W. Bennett in History of the Philosophy of 
Pedagogics, p. 2, a paper published by E. Stei- 
ger. New York, 1877.) 



11. 

ON EDUCATION. 

4. Man lives upon the earth as a member of a 
family, as a member of society, as a member of 
the state, and as an individual. These ethical re- 
lations and the natural surroundings constitute 
the environment which encircle and mould him. 
Whatever influence this environment has upon 
his native capacities and faculties to occasion 
them to grow into powers, or habits, is called 
Education. 

5. " We are born weak, we have need of help ; 
we are born destitute of every thing, we stand 
in need of assistance ; we are born stupid, we 
have need of understanding. All that we are not 
possessed of at our birth, and which we require 
when grown up, is bestowed on us by education. 
This education we receive from nature, from 
men, or from circumstances. The constitutional 
exertion of our organs and faculties is the educa- 
tion of nature ; the uses we are taught to make 
of that exertion constitute the education given 
us by men ; and in the acquisitions made by our 
own experience, on the objects that surround us, 
consists our education from circumstances. We 
are formed, therefore, by three kinds of masters. 



6 OK EDUCATION. 

The pupil, in whom the effects of their different 
lessons are contradictory, is badly educated, and 
can never be consistent with himself. He, in 
whom they are perfectly consonant, and always 
tend to the same point, hath only attained the 
end of a complete education. His life and ac- 
tions demonstrate this, and that he alone is well 
brought up. Of these three different kinds of 
education, that of nature depends not on our- 
selves ; and but in a certain degree that of cir- 
cumstances : the third, which belongs to men, is 
that only we have in our power : and even of 
this we are masters only in imagination ; for who 
can flatter himself he will be able entirely to gov- 
ern the discourse and actions of those who are 
about a child?" (Rousseau, JSmilius and So- 
phia, vol. 1, pp. 4, 5. London, 4 vols., 1783.) 
6. "Education is the influencing of man by 
man, and it has for its end to lead him to actual- 
ize himself through his own efforts. 
It is the nature of education only to assist in the 
producing of that which the subject would strive 
most earnestly to develop for himself if he had a 
clear idea of himself. . . . Man, therefore, 
is the only fit subject for education. We often 
speak, it is true, of the education of plants and 
animals ; but even when we do so, we apply, 
unconsciously perhaps, other expressions, as ' rais- 
ing ' and ' training, ' in order to distinguish these. 
The general form of Education is determined by 
the nature of the mind, that it really is nothing 
but what it makes itself to be. The mind is (1) 
immediate (or potential), but (2) it must 



02^ EDUCATIOJS". 7 

estrange itself from itself as it were, so that it 
may place itself over against itself as a special 
object of attention ; (3) this estrangement is fin- 
ally removed through a further acquaintance 
with the object. . . . Education cannot 
create : it can only help to develop to reality the 
previously existent possibility ; it can only help 
to bring forth to light the hidden life. 
Education seeks to transform every particular 
condition so that it shall no loncjer seem stransce 
to the mind or in any wise foreign to its own 
nature. This identity of consciousness, and the 
special character of any thing done or endured by 
it, we call Habit (habitual conduct or behavior). 
It conditions formally all progress ; for that 
which is not yet become habit, but which we 
perform with design and an exercise of our will, 
is not yet a part of ourselves. . . . The 
limits of Education are found in the idea of its 
nature, which is to fashion the individual into 
theoretical and practical rationality." (Rosen- 
kranz, Pedagogics as a System, pp. 7-23, ed. 
1872, St. Louis. Translated by Anna C. Brac- 
kett.) 

7. '' Education differs from information or 
knowledge. The latter is of a special character, 
the purport of which is to fit a man for bringing 
about certain definite results by the immediate 
operation of that knowledge which he possesses. 
We talk, indeed, of the education of a lawyer, 
a doctor, and a clergyman — of an engineer, a 
soldier, or a sailor ; generally meaning by it the 
information or knowledge which he has acquired 



8 OJ?" EDUCATION. 

for the immediate exercise of Ms vocation. But 
law, medicine, divinity, mechanics, strategics, 
and navigation, are not education. A man may 
possess any one of them and be well-nigh illite- 
rate, though of course some can more possibly 
co-exist with want of education than others. 
One can conceive that a man may have a pro- 
found practical acquaintance with law, and be an 
uneducated person. Again, to quote an in- 
stance, the first Duke of Marlborough was one 
of the most skilful generals ever known, but he 
could not spell, and hardly write. Some men 
who have had the most marvellous aptitude and 
quickness in mechanical science, have been un- 
able, from sheer ignorance, to sustain a common 
conversation. Education, on the other hand, 
deals with formalities. It does not so much 
aim at setting the mind right on particular points, 
as on getting the mind into the way of being 
right. It does not deal with matter, but with 
method. It purposes to train the thinking pow- 
ers of man, not to fill the mind with facts. 
Hence, were it perfect, it would cultivate the in- 
telligence so largely as to render easy the acqui- 
sition of any knowledge. It deals, in short, 
either directly or indirectly, with logical order 
and the reasoning powers. That it falls short of 
effecting w^hat it purposes, is due to defects 
in its system, to defects in man's mind, to de- 
fects in this or that man's mind. As, however, 
its operation is not immediate, but only indi- 
rect, its best methods are frequently cavilled at 
as useless. It may teach logical method of 



01^ EDUCATION-. 9 

thinking and reasoning. This, however, is gen- 
erally too abstract for most minds, except they 
be more or less matured, and more or less in- 
formed on some one or two subjects. In place 
of this, then, it teaches ordinarily something, 
which is as exact an illustration of logical 
method as can be, and which, being unfailing in 
its inferences, trains the mind in method, and 
often stores it with facts. In a greater or less 
degree, but in some degree at least, this inculca- 
tion of an abstract method is necessary for any 
kind of education, and even, except it be a mere 
knack, for information." (Rogers, Education 
in Oxford, pp. 1-3. London, 1861.) 

8. In the following quotation the extension 
of the term education is limited substantially to 
the work of the teacher. This limitation is un- 
usual, and the advantages gained by it are hard- 
ly evident : ' ' First, let me quote the definition 
(of Education) embodied in the ideal of the foun- 
ders of the Prussian National System. It is 
given shortly as ' the harmonious and equable 
evolution of the human powers ;' at more length, 
in the words of Stein, ' by a method based on 
the nature of the mind, every power of the soul 
to be unfolded, every crude principle of life 
stirred up and nourished, all one-sided culture 
avoided, and the impulses on Avhich the strength 
and worth of men rest, carefully attended to.' 
(Donaldson's Lectures on Education, p. 38.) 
This definition, which is pointed against narrow- 
ness generally, may have had special reference to 
the many omissions in the schooling of the fore- 



10 ON EDUCATION^. 

gone times : the leaving out of such things as 
bodily or muscular training ; training in the 
senses or observation ; training in art or refine- 
ment. It farther insinuates that hitherto the 
professed teacher may not have done much even 
for the intellect, for the hiofher moral trainino- 
nor for the training with a view to happiness or 
enjoyment. 

" In the very remarkable article on education 
contributed by James Mill to t\\Q Encycloiocedia 
Britannica, the end of education is stated to he 
* to render the individual, as much as possible, 
an instrument of happiness, first to himself, and 
next to other beings.' This, howev^er, should be 
given as an amended answer to the first question 
of the Westminster Catechism — ' What is the 
chief end of man ? ' The utmost that we could 
expect of the educator, who is not everybody, 
is to contribute his part to the promotion of hu- 
m:in happiness in the order stated. No doubt 
the definition goes more completely to the root 
of the matter than the German formula. It does 
not trouble itself with the harmony, the many- 
sidedness, the wholeness, of the individual de- 
velopment ; it would admit these just as might 
be requisite for securing the final end. 

" James i\[ill is not singular in his over-grasp- 
ing view of the subject. The most usual sub- 
division of Education is into Physical, Intellect- 
ual, Moral, Religious, Technical. ' Now when v>^e 
inquire into the meaning of Physical Education, 
we find it to mean the rearing of a healthy hu- 
man being, by all the arts and devices of nursing 



ON" EDUCATIOK. 11 

feeding, clothing, and general regimen. Mill in- 
cludes this subject in his article, and Mr. Her- 
bert Spencer devotes a very interesting chapter to 
it in his work on Education. It seems to me, 
however, that this department may be kept quite 
separate, important though it be. It does not 
at all depend upon the principles and considera- 
tions that the educator, properly so called, has in 
view in the carrying on of his work. The dis- 
cussion of the si>bject does not in any way help 
us in educational matters, as most commonly un- 
derstood ; nor does it derive any illumination 
from being placed side by side with the arts of 
the recognized teacher. The fact of bodily 
health or vigor is a leading postulate in bodily 
or mental training, but the trainer does not take 
upon himself to lay down the rules of hygiene. 

" The inadvertence, for so I regard it, of 
coupling the Art of Health with Education is eas- 
ily disposed of, and does not land us in any ard- 
uous controversies. Very different is another 
aspect of these definitions: that wherein the end 
of Education is propounded as the promotion of 
human happiness, human virtue, human perfec- 
tion. Probably the qualification will at once be 
conceded, that Education is but one of the means, 
a single contributing agency to the all-including 
end. Nevertheless, the openings for difference 
of opinion as to what constitutes happiness, vir- 
tue or perfection, are very wide. Moreover, the 
discussion has its proper place in Ethics and in 
Theology, and if brought into the field of Educa- 
tion, should be received under protest. 



12 01^ EDUCATIOiq'. 

'' Before entering upon tlie consideration of 
this difficulty, the greatest of all, I will advert to 
some of the other views of education that seem 
to err on the side of taking in too much. Here, 
I may quote from the younger Mill, who, like 
his father, and unlike the generality of theorists, 
starts more scientifico with a definition. Edu- 
cation, according to him, ' includes whatever we 
do for ourselves, and whatever is done for us by 
others, for the express purpose of bringing us 
nearer to the perfection of our nature ; in its 
largest acceptation, it comprehends even the in- 
direct efEects produced on character and on the 
human faculties by things of which the direct 
purposes are different ; by laws, by forms of 
government, by the industrial arts, by modes of 
social life ; nay even by physical facts not depen- 
dent on the human will ; by climate, soil, and 
local position.' lie admits, however, that this 
is a very wide view of the subject, and for his 
own immediate purpose advances a narrower 
view, namely, ' the culture which each genera- 
tion purposely gives to those who are to be its 
successors, in order to qualify them for at least 
keeping up, and if possible for raising, the im- 
provement which has been attained. ' (^Inaugu- 
ral Address at St. Andreio''s, p. 4.) 

" Besides involving the dispute as to what 
constitutes ' perfection, ' the first and larger state- 
ment is, I think, too wide for the most compre- 
hensive Philosophy of Education. The influ- 
ences exerted on the human character by climate 
and geographical position, by arts, laws, govern- 



OK EDUCATION. 13 

ment and modes of social life, constitute a very 
interesting department of Sociology, and have 
their place there and nowhere else. What we 
do for ourselves, and what others do for us, to 
bring us nearer to the perfection of our nature, 
may be education in a precise sense of the word, 
and it may not. I do not see the propriety of - 
including under the subject the direct operation 
of rewards and punishments. No doubt we do 
something to educate ourselves, and society does 
something to educate us, in a sufficiently proper 
acceptation of the word ; but the ordinary influ- 
ence of society, in the dispensing of punishment 
and reward, is not the essential fact of Educa- 
tion, as I propose to regard it, although an ad- 
junct to some of its legitimate functions. 

" Mill's narrow expression of the scope of the 
subject is not exactly erroneous ; the moulding 
of each generation by the one preceding is not 
improperly described as an Education. It is, 
however, grandiose rather than scientific. Noth- 
ing is to be got out of it. It does not give the 
lead to the subsequent exposition. 

" I find in the article ' Education,' in Cham- 
bers^ s Encyclopcedia, a definition to the following 
effect : ' In the widest sense of the word a man 
is educated, either for good or for evil, by 
every thing that he experiences from the cradle 
to the grave [say, rather, " formed," " made," 
"influenced"]. But in the more limited and 
usual sense, the term Education is confined to 
the efforts made, of set purpose, to train men in 
a particular way — the efforts of the grown-up 



14 Oiq- EDUCATION. 

part of tlie community to inform tlie intellect 
and mould the character of the young [rather too 
much stress on the fact of influence from with- 
out] ; and more especially to the labours of pro- 
fessional educators or schoolmasters.' The con- 
cluding clause is the nearest to the point — the 
arts and methods employed by the schoolmas- 
ters ; for, although he is not alone in the work 
that he is expressly devoted to, yet he it is that 
typifies the process in its greatest singleness and 
purity. If by any investigations, inventions or 
discussions, we can improve his art to the ideal 
pitch, we shall have done nearly all that can be 
required of a science and art of Education." 
(Bain, Education as a Science, Art. I., in Mindj 
pp. 1-4, No. 5, January, 1877.) 

9. " The true view of education is to regard 
it as a course of training. The youth in a gymna- 
sium practises upon the horizontal bar, in order 
to develop his muscular powers generally ; he- 
does not intend to go on posturing upon hori- 
zontal bars all through life. School is a place 
where the mental fibres are to be exercised, 
trained, expanded, developed, and strength- 
ened. . . . It is the very purpose of a lib- 
eral education, as it is correctly called, to de- 
velop" and train the plastic fibres of the youthful 
brain, so as to prevent them taking too early a 
definite ' set,' which will afterwards narrow and 
restrict the range of acquisition and judgment. 
I will even go so far as to say that it is hardly 
desirable for the actual things taught at school 
to stay in the mind for life. The source of 



Oiq^ EDUCATION. 15 

error is the failure to distinguish between the 
form and the matter of knowledge, between the 
facts themselves and the manner in which the 
mental powers deal with facts. . . . It is 
the purpose of education so to exercise the fac- 
ulties of mind that the infinitely various experi- 
ence of after-life may be observed and reasoned 
upon to the best effect." (Jevons, in Mind, 
pp. 197-207, No. VI., April, 1877.) (Rein- 
serted under " Memory and Cram," § 172.) 

10. *' Educit obstetrix, educat nutrix, insti- 
tuit pedagogus, docet magister." (Varro. 
See also Aii. and SVd Lat. Lex., unabridged.) 

11. " Training (Fr. trainer) is development 
by instruction, exercise, and discipline, and is 
applicable to the whole nature of a man, or, 
specifically, to the faculties which he possesses. 
It denotes no more than a process of purposed 
habituation, and is equally applicable to the phy- 
sical and mental powers, so that it may include 
both at the same time." (Smith, Syn. Discri- 
minated, Art. Education, ed. 1878.) This 
sense of training is the ordinary meaning now 
attached to education. 

12. "A thorough and complete education 
ought to preserve and increase the pupil's bodily 
health and strength ; give him command of his 
own muscular and mental powers ; increase his 
quickness in perceiving through his five senses, 
and quicken his mental perception ; form in him 
the habit of prompt and accurate judgment ; 
lead to delicacy and depth in every right feel- 
ino- • and make him inflexible in his conscien- 



16 01^ EDUCATION^. 

tious and steadfast devotion to all liis duties. 
In other words, an integral education must in- 
clude at least these four branches : — gymnastics, 
or care of the body ; noetics, or training of the 
mind ; aesthetics, or cultivation of the tastes ; 
and ethics, which shall include religion as well 
as duty. And in every part of each branch of 
education, there will be a double end in view, 
namely, the increase of knowledge, and the in- 
crease of skill. Each study may be made the 
object of thought, or the object of action ; in 
the one case it is pursued as a science ; in the 
other case as an art." (Thomas Hill, The True 
Order of Studies, pp. 1, 8, ed. 1876.) 

13. '' The conclusions of the honest and in- 
telligent inquirer after the truth in this matter, 
will be something like the following : — That edu- 
cation (from e and duco, to lead forth) is devel- 
opment ; that it is not instruction merely — 
knowledge, facts, rules — communicated by the 
teacher, but it is discipline, it is a waking up 
of the mind, a growth of the mind, — growth by 
a healthy assimilation of wholesome aliment. It 
is an inspiring of the mind with a thirst for 
knowledge, growth, enlargement, — and then a dis- 
ciplining of its powers so far that it can go on to 
educate itself. It is the arousing of the child's 
mind to think, without thinking for it ; it is the 
awakening of its powers to observe, to remem- 
ber, to reflect, to combine. It is not a cultiva- 
tion of the memory to the neglect of every thing 
else ; but it is a calling forth of all the faculties 
into harmonious action. If to possess facts sim- 



OK EDUCATION. 17 

ply is education, then an encyclopaedia is better 
educated than a man.'^ (Page, Theory and 
Practice of Teaching , p. 70, ed. 1853.) 

14. " Suppose it were perfectly certain that 
the life and fortune of every one of us would, 
one day or other, depend upon his winning or 
losing a game at chess. Don't you think that 
we should all consider it to be a primary duty to 
learn at least the names and the moves of the 
pieces ; to have a notion of a gambit, and a keen 
eye for all the means of giving and getting out 
of check ? Do you not think that we should 
look with disapprobation amounting to scorn, 
upon the father who allowed his son, or the 
state which allowed its members, to grow up 
without knowing a pawn from a knight ? 

*' Yet it is a very plain and elementary truth, 
that the life, the fortune, and the happiness of 
every one of us, and, more or less, of those who 
are connected with us, do depend upon our 
knowing something of the rules of a game infin- 
itely more difficult and complicated than chess. 
It is a game which has been played for untold 
ages, every man and woman of us being one of 
the two players in a game of his or her own. 
The chess-board is the world, the pieces are the 
phenomena of the universe, the rules of the 
game are what we call the laws of Nature. The 
player on the other side is hidden from us. 
We know that his play is always fair, just, and 
patient. But also we know, to our cost, that 
he never overlooks a mistake, or makes the small- 
est allowance for ignorance. To the man who 



18 ON" EDUCATION". 

plays well the higliest stakes are paid, with that 
sort of overflowing generosity with which the 
strong shows delight in strength. And one who 
plays ill is checkmated — without haste, but with- 
out remorse. 

" My metaphor will remind some of you of 
the famous picture in which Retzsch has de- 
picted Satan playing at chess with man for his 
soul. Substitute for the mocking fiend in that 
picture, a calm, strong angel who is playing for 
love, as we say, and would rather lose than win 
— and I should accept it as an image of human 
life. 

" Well, what I mean by Education is learning 
the rules of this mighty game. In other words, 
education is the instruction of the intellect in the 
laws of Nature, under which name I include not 
merely things and their forces, but men and 
their ways ; and the fashioning of the affections 
and of the will into an earnest and loving desire 
to move in harmony witli -those laws. For me, 
education means neither more nor less than this. 
Any thing which professes to call itself education 
must be tried by this standard, and if it fails to 
stand the test, I will not call it education, what- 
ever may be the force of authority, or of num- 
bers, upon the other side. 

" It is important to remember that, in strict- 
ness, there is no such thing as an uneducated 
man. Take an extreme case. Suppose that an 
adult man, in the full vigour of his faculties, 
could be suddenly placed in the world, as Adam 
is said to have been, and then left to do as he 



OH EDUCATIOi^. 19 

best might. How long would lie be left unedu- 
cated ? Not five minutes. Nature would begin 
to teach him, through the eye, the ear, the 
touch, the properties of objects. Pain and 
pleasure would be at his elbow telling him to do 
this and avoid that ; and by slow degrees the 
man would receive an education, which, if nar- 
row, would be thorough, real, and adequate to 
his circumstances, though there would be no ex- 
tras and very few accomplishments. 
The great mass of mankind are the ' Poll,' who 
pick up just enough to get through without much 
discredit. Those who won't learn at all are 
plucked ; and then you can't come up again. 
Nature's pluck means extermination. 
Nature's discipline is not even a word and a 
blow, and the blow first ; but the blow without 
the word. It is left to you to find out why your 
ears are boxed." (Huxley, Zay Sermons, pp. 
31-84, ed. 18V0. Lqiidon.) 

15. "As theory, Education alhes itself to 
Psychology, Physiology, and Sociology. The 
materials of its teaching it draws from these phi- 
losophies, from the practice of the schoolroom, 
and from the rich domain of History. 
I have some sympathy with the cynical Love 
Peacock, who, in describing certain social bores 
in the shape of men of one idea who hold forth 
in season and out of season, says : — ' The worst 
of all bores was the third. His subject had no 
beginning, middle, nor end. It was Education. 
Never was such a journey through the desert 
of mind, the great Sahara of intellect. The 



20 01^ EDUCATION. 

very recollection makes me thirsty.' Such men 
are not educationists in any sense in which that 
term is applicable within these walls. They are 
men of leisure who have restless minds, and if 
they have not one fixed idea or crotchet, will 
find another. An educationist has no crotchets. 
That man has crotchets who, having seized on 
that particular corner of a large and many-sided 
subject which has some secret affinity with his 
own mind, or affords the quickest passage to no- 
toriety, pursues it to the death. Now, an edu- 
cationist is, by virtue of his very name and vo- 
cation, inaccessible to all petty fanaticisms. He 
has to deal with a subject of infinite variety, and 
so variously related to life, that he is more apt 
to be lost in hesitations and scepticisms than to 
be the victim of a fixed idea. If you wish to 
meet with educational crotchets, you must go to 
the specialist in this or that department of 
knowledge, who is unfortunate enough to take 
up the question of Education, as you see he 
often in moments of aberration takes up other 
subjects which are outside his own range of in- 
tellectual experience. It is only in such cases 
that you will find the confidence and self-assur- 
ance which is born of limited knowledge, and 
the pertinacious insistence which flows from 
these habits of mind. To him whose subject is 
Education crotchets are prohibited, because his 
opinions on this or that point are related on the 
one side to rational and comprehensive theory, 
and on the other to the daily practice of the 
schoolroom and the needs of life. 



OK EDUCATION. 21 

The more abstract treatment of the theory of Ed- 
ucation is doubtless, if true in its philosophy, of 
universal application. It sweeps the whole field. 
But this will engage our attention only within 
carefully prescribed limits, and when we leave 
this portion of our subject, Ave have to restrict 
ourselves on all sides. The education of every 
human being is determined by potent influences 
Avhicli do not properly fall within the range of 
our consideration here. The breed of men to 
which the child belongs, the character of his pa- 
rents, the human society into which he is born, 
the physical circumstances by which he is sur- 
rounded, are silently but irresistibly forming 
him. The traditions of his country, its popular 
literature, its very idioms of speech, its laws and 
customs, its religious life, its family life, consti- 
tute an aggregate of influence which chiefly 
make him what he is. . . . By their con- 
stant presence they mould the future man, him- 
self unconscious. They are the atmosphere of 
the humanity of his particular time and place, 
and in breathing it he is essentially a passive 
agent. . . . The passive activity of our na- 
ture is not to be ignored in our educational 
methods ; it is to be turned to use as one of our 
most potent instruments, but it is mainly the 
self-conscious forces that we have to educe and 
direct. Even in doing this we are bound by ex- 
ternal conditions, and must take note not only of 
the almost irresistible forces around us, but of 
minor conditions of time, place, and circum- 
stance. Each successive century, and the tra- 



22 OK EDCJCATIOiT. 

ditions and circumstances of each country, nay, 
tlie genius of each people, present to us the ed- 
ucational problem in ever-changing aspects. 
Educational systems cannot be manufactured in 
the study. Our theory of the end of all educa- 
tion and the means by which that end has to be 
attained may be, or rather ought to be, always 
the same ; but the application of that theory 
must vary Avith varying external conditions. 
What present defects have we here and now, 
and to what dangers are we exposed ? is the 
form which the practical question must take with 
us." (jLanrie, Inaufftiral Addi^ess, Chair of Ed- 
ucation, pp. 21-24. Edinburgh, 1876.) 

16. " To write upon education, means to 
write upon almost every thing at once ; for it has 
to care for, and watch over, the development 
of an entire, though miniature, world in little, 
— a microcosm of the microcosm. All the ener- 
gies with which nations have labored and signal- 
ized themselves once existed as germs in the 
hand of the educator. *If we carried the sub- 
ject still further, every century, every nation, 
and even every boy and every girl, would require 
a distinct system of education, a different primer, 
and domestic French governess, &c. . . . But 
although the spirit of education, always watch- 
ing over the whole, is nothing more than an en- 
deavor to liberate, by means of a freeman, the 
ideal human being which lies concealed in every 
child ; and though, in the application of the di- 
vine to the child's nature, it must scorn some 
useful things, some seasonable, individual, or im- 



OK EDUCATION. 23 

mediate ends ; yet it must incorporate itself in 
tlie most definite applications, in order to be 
clearly manifested. 

" But who then educates in nations and 
ages ? — Both ! — The living time, which for 
twenty or thirty years struggles unceasingly with 
men through actions and opinions, tossing them 
to and fro as with a sea of waves, must soon 
wash away or cover the precipitate of the short 
school years, in which only one man, and only 
words taught. The century is the spiritual cli- 
mate of man, mere education the hot-house and 
forcing-pit, out of which he is taken and planted 
forever in the other. By century is here meant 
the real century, which may as often- truly con- 
sist of ten years, as of ten thousand, and which 
is dated, like religious eras, only from great men. 
What can insulated words do against living pres- 
ent action ? The present has for new deeds 
also new words ; the teacher has only dead lan- 
guages for the, to all appearance, dead bodies of 
his examples. The educator has himself been 
educated, and is already possessed, even without 
his knowledge, by the spirit of the age, which he 
assiduously labors to banish out of the youth (as 
a wliole city criticises the spirit of the whole 
city). Only, alas ! every one believes himself to 
stand so precisely and accurately in the zenith of 
the universe, that, according to his calculation, 
all suns and nations must culminate over his 
head ; and he himself, like the countries at the 
equator, cast no shadow save into himself 
alone. . . . The spirit of the nation and of 



24 ON- EDUCATION. 

the age decides, and is at once the schoohnaster 
and the school ; for it seizes on the pupil to 
form him with two vigorous hands and powers ; 
with the living lesson of action, and with its 
unalterable unity. If — to begin with unity — ed- 
ucation must be, like the Testament, a continu- 
ous endeavor to withdraw the force of interrupt- 
ing mixtures, then nothing builds up so strong as 
the present, which ceases not for a moment, and 
eternally repeats itself ; and which, with joy and 
sorrow, with towns and books, with friends and 
enemies, in short, with thousand-handed life, 
presses and seizes on us. No teacher of the peo- 
ple continues so uniformly one with himself as 
the teaching people. Minds molten into masses 
lose something of their free movements : which 
bodies, for instance, that of the world, perhaps 
that of the universe, seem to gain by their very 
massiveness, and, like a heavy colossus, to move 
all the more easily along the old, iron-covered 
track. For however mach marriages, old age, 
deaths and enmities, are in the individual case 
subject to the law of freedom, yet in a whole na- 
tion, lists of births and deaths can be made, by 
w^hich it may be shown that in the canton of 
Berne (according to Mad. de Stael) the number 
of divorces, as in Italy that of murders, is the 
same from year to year. Must not, now, the 
little human being placed on such an eternally 
and ever similarly acting world, be borne as 
upon a flying earth, where the only directions 
that a teacher can give avail nothing, because he 



OK EDUCATION. 25 

has first unconsciously received liis line of move- 
ment upon it ? 

' ' Thence, in spite of all reformers and inform- 
ers, nations, like meadows, reach ever a similar 
verdure ; thence, even in capital cities, where all 
school-books and schoolmasters, and even par- 
ents of every kind, educate, the spirit main- 
tains itself unalterably the same. Repetition is 
the mother not only of study, but also of educa- 
tion. . . . Certainly one might say that also 
in families there educates, besides the popular 
masses, a pedagogic crowd of people ; at least, 
for instance, aunt, grandfathers, grandmothers, 
father, mother, god-parents, friends of the fam- 
ily, the yearly domestics, and at the end of all 
the instructor beckons with his forefinger, so that 
— could this force continue as long as it would 
gladly be maintained — a child, under these many 
masters, would resemble, much more than one 
thinks, an Indian slave, who wanders about with 
the inburnt stamps of his various masters. But 
how does the multitude disappear compared 
with the higher one, by which it was colored ; 
just as all the burnt marks of the slave yet can- 
not overcome the hot black coloring of the sun, 
but receive it as a coat of arms in a sable field ? 
. . . The end desired must be known before 
the way. All means or arts of education will 
be, in the first instance, determined by the ideal 
or archetype we entertain of it. But there floats 
before common parents, instead of one arche- 
type, a whole picture cabinet of ideals, which 
they impart bit by bit, and tattoo into their 



26 OK EDUCATION. 

children. If tlie secret variances of a large class 
of ordinary fathers Avere brought to light, and 
laid down as a plan of studies, and reading cata- 
logue for a moral education, they would run 
somewhat after this fashion : — In the first hour 
pure morality must be read to the child, either 
by myself, or the tutor ; in the second, mixed 
morality, or that which may be applied to one's 
own advantage ; in the third, ' Do you not see 
that your father does so and so ? ' in the fourth, 
' You are little, and this is only fit for gro'^vn- 
up people ;' in the fifth, ' The chief matter is 
that you should succeed in the Avorld, and be- 
come something in the state ;' in the sixth, 
* Not the temporary, but the eternal, determines 
the worth of a man ;' in the seventh, ' Therefore 
rather suffer injustice, and be kind ;' in the 
eighth, ' but defend yourself bravely if any one 
attack you ;' in the ninth, ' Do not make such a 
noise, dear child ;' in the tenth, ' A boy must 
not sit so quiet ;' in the eleventh, ' You must 
obey your parents better ;' in the twelfth, ' and 
educate yourself. ' So by the hourly change of 
his principles the father conceals their untena- 
bleness and one-sidedness. As for his wife, she 
is neither like him, nor yet like that harlequin 
who came on to the stage with a bundle of pa- 
pers under each arm, and answered to the in- 
quiry what he had under his right arm, ' orders,' 
and to what he had under his left, ' counter- 
orders ;' but the mother might be much better 
compared to a giant Briareus, who had a hun- 
dred arms, and a bundle of papers under each. 



OK EDUCATION. 27 

The majority of educated men are, 
therefore, at present an iUuraination which burns 
oif by fits and starts in the rain, shining with in- 
terrupted forms, and depicting broken charac- 
ters. But the bad and impure spirits of educa- 
tional systems are yet to be reduced into other 
divisions. Many parents educate their children 
only for themselves, — that is, to be pretty 
blocks, or soul-alarums, which are not set to 
move or sound when stillness is required. The 
child has merely to be that on which the teacher 
can sleep most softly or drum most loudly ; who, 
having something else to do and to enjoy, wishes 
to be spared the trouble of education, duly but 
most unreasonably expecting its fruits. 
Related to those teachers who wished to be ma- 
chine-makers are the educators for appearances 
and political usefulness. Their maxims, thor- 
oughly carried out, would -only produce pupils, 
or rather sucklings, passively obedient, boneless, 
well-trained, patient of all things, — the thick, 
hard, human kernel would give place to the 
soft, sweet fruit-pulp, — and the child's clod of 
earth, into which growing life should breathe a 
divine spirit, would be kept down and manured 
as though it were but a corn-field, — the edifice 
of the state would be inhabited by mere spin- 
ning-machines, calculating-machines, printing 
and pumping apparatus, oil-mills, and models 
for mills, pumps, and spinning-machines, &c. 
Education can neither entirely consist 
of mere unfolding in general, or, as it is now 
better called, excitement, — for every continued 



28 01^ EDUCATION". 

existence unfolds, and every bad education ex- 
cites, just as oxygen positively irritates, — nor in 
the unfolding of al! the powers, because we can 
never act upon the whole amount of them at 
once ; as little as in the body susceptibility and 
spontaneity, or the muscular and nervous system, 
can be strengthened at the same time." (Rich- 
ter, Levana, Preface, ix, and pp. 7-33. Boston. 
1863.) 

17. "A treatise on education does not in- 
clude the theory of instruction, whose wide realm 
embraces the mistakes of all sciences and arts ; 
nor the theory of remedies, which would require 
libraries instead of volumes for the complication 
of mistakes, years, positions, and relations. At 
the same time no science is entirely disconnected 
from the rest ; the feet cannot move without the 
hands." {Ibid., p. 390.) 

18. The education that any one receives de- 
pends upon the ethical relations by which he is 
surrounded. But education must regard the 
nature and powers of the mind of him who is to 
be educated. Hence education, as a product, is 
founded upon ethical relations upon the one 
hand, and the nature of mind, or Psychology, 
upon the other. Education, in part, is depend- 
ent upon teaching or instruction as a means for 
securing its ends. Teaching, then, directly 
busies itself with the subject-matter that is to be 
learned, and with the mind which is to learn it. 

19. " The educator of youth does not merely 
communicate so much instruction from year to 
year ; he develops the receptive and acquisitive 



01^ EDUCATION". 29 

tendencies of mind, which are afterwards to 
play their part in the intellectual activity of the 
nation. He trains the intelligence of those who 
are afterwards to be the teachers of others, as 
well as of those who are only to be interested in- 
quirers after truth." (Calderwood, On Teach- 
ing, p. 49, ed. 1875, New York.) 



III. 

ON TEACHING. 

20. Having briefly considered tlie notion of 
the terms Pedagogics and Education, the reader 
is directed to the conception of the term Teach- 
ing, 

Thought is the modification of the activity 
called Intelligence, and Language is its Form. 
Language is the mirror which reflects the ideas 
that are in the mind of him who utters it. Lan- 
guage is a record of thought. Language, in its 
widest signification, is the instrument for per- 
petuating the life of a nation, or rather it is the 
life of a people perpetuated. Language is the 
form of the matter which once existed in the 
consciousness of the person who uttered it ; it is 
a product of thought ; perhaps more exactly it 
is thought itself. ''It is only as there is a 
A.O}/o5 in the outer world, answering to the 
\oyoS or internal reason of the parties, that men 
can come into a mutual understanding in regard 
to any thought-state whatever." (Grindon, 
Life, p. 349.) 

" By Language we do not mean the mere art 
of speaking and writing according to some 
specific, arbitrary mode, which though intelli- 



OK TEACHING. 31 

gible in one country, is unintelligible in another. 
We mean that beautiful and inevitable flowering 
forth inr speech of the inner, living intellect of 
man, which, older and more excellent than all 
prosody and spelling, is an integral work of na- 
ture ; and which, were it possible for the acci- 
dental forms which it may hold at any given 
epoch, as English and French, Latin and Greek, 
to be suddenly and totally abolished, would in 
itself be unaffected, and speedily incarnate 
afresh, unchanged save" in the extrinsic circum- 
stances of costume." (^Ihid, pp. 153, 154, third 
ed., London.) Nations differ in their language 
— these differences measure those differences 
that exist among the ideas or notions which are 
substantially common to many peoples. The 
content and extent of words having the same 
general meaning, when expressed in different 
languages, are hardly equivalent nor precisely 
identical. No two nations live and act exactly 
alike, and as language follows life, it is but in 
the harmony of things that this should occasion 
different notions of life and actions in the minds 
of the various peoples, and hence in language. 
Two or three examples will illustrate the case : 

21. To indicate a certain notion, the Greeks 
used deiknumi, the English equivalents of which 
are : " To bring to light, to display, to portray, 
to represent to the life as in statuary, to shew, 
to point out, to make known by words, to tell, 
to explain, to teach, to prove, to offer, to prof- 
fer. " Battmann traces the prefix deik to a root 
dek, which contains the common notion of 



32 OK teachi:n^g. 

stretching out the right hand either to point, 
or to welcome. (Liddell and Scott, Greek- 
English Lexicon, Oxford, 1871.) The essential 
idea seems to rest upon the action of pointing 
to, or towards, a thing. The Greeks cultivated 
the graces of action as well as the harmony of 
sounds, and it is not difficult to conceive the 
elders among the people pointing out, showing, 
portraying as artists, the things before them to 
the youth, much as a traveller would do at the 
present time to a youthful companion. The fact 
that Socrates was at so great pains to develop in 
his pupils the power to reason would argue that, 
in his opinion, before his time the powers of per- 
ception and memory of the youth had been rec- 
ognized as of greater value in acquiring an edu- 
cation than the reflective powers. The word 
teaching also appears to exhibit some one as in 
the action of directing the attention of another 
to something through, or by means of, the ges- 
tures of his right hand — it does not so much 
seem to exhibit one as showing a thing, object, 
immediately and directly, as it shows indirectly 
through words and general gestures, and by illus- 
trative sketches — it implies an exhortation to at- 
tend to this thing which is in mind as a philo- 
sophical truth. It would seem to indicate an ex- 
planation of memorized words. ""When the 
children could read, and understand what they 
read, the works of the poets were put in requi- 
sition, to exercise their minds, and awaken their 
hearts to great and noble deeds. Plato, Leg. 
vii. p. 810, approves of this, and also recom- 



O:^ TEACHING. 33 

mends committing whole poems, or select pas- 
sages, to memory ; and tliis method of instruc- 
tion appears to have been universal. Above all, 
the poems of Homer were thought to contain, 
by precept and example, every thing calculated 
to awaken national spirit, and to instruct a man 
how to be beautiful and good." (Becker, 
Charicles, trans, by Frederick Metcalfe, ed. 
1866, p. 233.) 

22. The Latins conveyed a certain notion by 
doceo, which is rendered in English by : "To 
teach, to inform, to instruct, to show, to point 
out, to represent, to exhibit." It is compared 
with edocere, which means " to make one learn, 
to make acquainted with, more energetic than 
docere." Perdccere means " to teach per- 
fectly, to instruct thoroughly." Erudire im- 
plies " to initiate in learning." Instruct, in and 
struo, means : To join together, to pile up, 
heap up, to erect, to build, to set in array, to 
join together, to construct. (Bullion, Lat.-Eng. 
Dict.y ed. 1869.) The essential idea with the 
Latins seems to be that of laying before one 
some matters as objects to be seen, handled, 
piled up in layers one upon another (instruct), 
to show as in an exhibition. The word pictures 
one as standing at work upon some visible ob- 
jects, and calling the attention of another to these 
objects as he piles them up, one upon another. 
This sense is virtually different from the thought 
with the Greeks, who rather withdrew them- 
selves from the presence of the things about 
wbicli they discoursed, and crowded the thought 



34 Oiq" TEACHING. 

home to tlie conviction of the hearer by words 
and exhortatory gestures of the right hand. 
This notion of doceo corresponds with the gene- 
ral characteristics of the Latins, who were a peo- 
ple pre-eminently skilful in the affairs of practi- 
cal business. They regarded the objects of bus- 
iness directly, rather than through philosophy. 
Hence, the one would instruct a youth in law by 
exhibiting to him law practice in the courts, 
while the other would lecture the youth about 
the principles of law in the abstract, while seated 
in his stone chair, or while Avalking about the 
groves. 

23. The Anglo-Saxons expressed a certain 
notion by the word t^can, which is rendered in 
English : '' To teach, to instruct, to show, to di- 
rect, to command, to see to, to provide, to or- 
der, to convince, to prove." (Bosworth, An- 
glo-Saxon and Eng. Bict.j London, 1860.) Li 
this case the notion has an element of power and 
authority in it ; it shows, with power to com- 
mand attention ; it directs, but it is imperative 
about something towards somebody ; it does not 
simpl}^ exhort the attention of somebody towards 
an idea by the right hand in persuasion or wel- 
come, as does the Greek deiknumi — nor does 
it call the attention of somebody to what the ex- 
hibitor has before him, piling it up in order, as 
do the Latin doceo and instruo ; but it shows 
something to somebody, meaning that this some- 
body shall attend to this something. This word 
t^can discloses the characteristic trait of the 
Anglo-Saxon life, the disposition to do something 



OK TEACHIKG. 35 

for another, and then to command liim to respect 
what has been placed before him. The word re- 
gards with emphasis both what is provided, and 
him for whom it is provided. 

24. These three instances iUustrate the differ- 
ences which exist among peoples when they ex- 
press a notion that is ordinarily regarded as the 
same by them all. Each people has its own set- 
ting of thoughts which control the form, and as- 
sist in conserving the meaning of subsequent no- 
tions. These thoughts, notions, conserved in 
form, are language. The words " instruct " and 
" teach" are both in common use at this time, 
practically as synonyms. Following the lines of 
their ancestry, and considering the tendency of 
the present age, it is determined to use the word 
teaching rather than instruction in the expres- 
sion Methods of Teaching, As illustrating the 
deep-seated element of authority which exists in 
the Anglo-Saxon notion of teaching, the follow- 
ing quotations are subjoined : 

25. "I hope I may be excused for one re- 
mark on a tendency in education at present, 
more especially with regard to the modern sub- 
jects, to render the process interesting, as it is 
usually called, but amusing would probably be 
the more correct word. It would be absurd to 
recommend that any subject should be proposed 
in a purposely repulsive form to students, espec- 
ially to youth ; but, on the other hand, it seems 
to me a most enervating practice to shrink from 
demanding even irksome attention whenever it is 
necessary. The lesson that success in any pur- 



36 OK TEACHII^^G. 

suit demands serious toil must be learned eventu- 
ally, and like most lessons is learned with least 
pain in early years." (Todliunter, Confiict of 
Studies and other Essays, p. 21. London, 
1873.) 

26. '* Parents and the public have little idea 
how close a resemblance there is between teach- 
ing and writing on the sands of the sea, unless 
either there is a distinct capacity for learning on 
the part of the pupil, or some • system of ex- 
amination and reward to force the pupil to ap- 
ply." (Jevons, paper in Mind, p. 195, No. VI., 
April, 1877.) (Reinserted under Memory and 
"Cram," § 172.) 

27. " Whatever the age and attainment of 
the- pupils under charge, the first requisite for 
communicating instruction is to gain and keep 
their attention. Teaching, to be successful, 
must therefore be adapted to win attention. At 
the earlier stages of school life this is the one 
pressing requirc-ment. Somehow, attention must 
be made possible even to the most restless little 
ones, to whom the first restraints of school life 
are irksome. Accustomed to have every new 
object attract their interest just as long as they 
recognized any thing attractive in it — permitted 
to change from one engagement to another as 
caprice dictated — they must be made familiar 
with restriction. They must begin to be regu- 
lated by the will of another. Taking this as 
self-evident, we are prone to say that they must 
do so, whether they will or not. This is one of 
our superficial current phrases which cover over 



OK TEACHIKG. 37 

many points needing careful consideration. At- 
tention is not to be secured by mere exercise of 
authority. Authority has a great deal to do 
through the whole course of school life, but we 
cannot * command ' attention, as we say, by 
merely demanding that it be given. A radical 
mistake is made if a teacher lean on his authority 
in the school as the guarantee for attention by the 
scholars. He must consider the requirements 
of the undisciplined mind, and adapt himself to 
them. Children attend to what interests them. 
This must determine the kind of assistance to 
be given them in acquiring habits of attention. 
To help them in this is an obvious part of a 
teacher's work. . . . The master of a school 
in this respect shares a task which is common to 
all who essay to teach others. In this appears 
the true place and power of the profession." 
(Calderwood, On Teaching, pp. 47-49, ed. 1875.) 
28. The conception of Teaching which pre- 
vails in these inquiries is limited to that assistance 
which one person (teacher) consciously gives to 
another person or thing (learner), when this lat- 
ter is learning something. Teachers are not 
necessarily educators. Any thing educates the 
child that helps to mould its character, or that 
stimulates its self-control. Fire educates in an 
imperative manner, but it does not teach. The 
authority of the parent educates his child, while 
the child may be taught nothing in regard to the 
nature or source of authority. A teacher's per- 
sonal influence may educate a school in ways of 
virtue, while he has taught them nothing about the 



38 OK TEACHING. 

nature of virtue. Teaching regards the purely 
intellectual capacities of Man. Education refers 
to all the capabilities of Mind. The intellect is 
taught by a person, and educated by persons and 
things. The will is educated by any power. 
Teaching sets the subject-matter, trusting the 
mind to accept the truth ; educating may exert 
a power without giving any reason or instruc- 
tion. Teachers should be educators. Parents 
are educators — they may also be teachers. Good 
teaching and good educating put the mind of 
him who is taught or educated, into a frame 
which acknowledges and accepts testimony and 
authority from whatever source they spring. 
That teaching or educating is pernicious which 
leaves the mind of the learner in a state of un- 
due skepticism towards testimony and authority. 
(See §§ 31-34.) 

29. " The communication of knowledge in 
general is the common idea by which these 
words — inform^ instruct, teach — are connect- 
ed with each other. Inform is the general term ; 
the other two are speciiick. To inform is the 
act of persons in all conditions ; to instruct and 
teach are the acts of superiours, either on one 
ground or another : one informs by virtue of an 
accidental superiority or priority of knowledge ; 
one instructs by virtue of superior knowledge, 
or superior station : one teaches by virtue of 
superiour knowledge, rather than station : diplo- 
matick agents inform their governments of the po- 
litical transactions in which they are concerned ; 
government instructs its different functionaries 



OK teachi:n^g. 39 

and officers in regard to their mode of proceed- 
ing ; professors and preceptors teach those who 
attend a publick school to learn. 

' ' To inform is applicable to matters of general 
interest ; we may inform ourselves or others on 
every thing which is a subject of inquiry or curios- 
ity ; and the inforniatiou serves either to amuse 
or to improve the mind ; to instruct is applica- 
ble to matters of serious concern, or that which 
is practically useful ; it serves to set us right in 
the path of life. A parent instructs his child in 
the course of conduct he should pursue ; a good 
child profits by the instruction of a good parent 
to make him wiser and better for the time to 
come ; to teach respects matters of art and 
science ; the learner depends upon the teacher 
for the formation of his mind, and the establish- 
ment of his principles. Every one ought to be 
properly informed before he pretends to give an 
opinion ; the young and inexperienced must be 
instructed before they can act ; the ignorant 
must be taught, in order to guard them against 
errour. Truth and sincerity are all that is neces- 
sary for an informant ; general experience and 
a perfect knowledge of the subject in question 
are requisite for the instructer; fundamental 
knowledge is requisite for the teacher. Those 
who give information upon the authority of 
others are liable to mislead ; those who instruct 
others in doing that which is bad, scandalously 
abuse the authority that is reposed in them ; 
those who pretend to teach what they themselves 



40 01^ TEACHII^G. 

do not understand, mostly betray tlieir ignorance 
sooner or later. 

*' To inform and to teach are employed for 
tilings as well as persons ; to instruct only for 
persons : books and reading inform the mind ; 
history or experience teaches mankind. ' ' (Crabb, 
Synonyms, ed. 1859.) 

30. "Inform (Lat. in and forma, shape or 
form) relates only to matters of fact made known 
to one who could not have known them before. 
Instruction (Lat. instruere, instructus) relates 
to principles drawn from known facts. Teach- 
ing (A. S. t«can, to teach), as distinct from 
instruction, is applied to practice (it may be the 
practice of an art or branch of knowledge). A 
child is instructed in grammar, and taught to 
speak a language. Teach has a purely mechani- 
cal application, which does not belong to instruct. 
A dog may be taught a trick ; but he could not 
be instructed in any thing. The two processes 
of teaching and instruction may thus go on 
simultaneously. In mathematics there is no in- 
formation, because the propositions are not state- 
ments of fact, but are based upon principles 
assumed. Information is of new facts ; instruc- 
tion is of undeveloped truths. Information 
extends knowledge ; instruction gives additional 
understanding ; teaching, additional power of 
doing. Acquaint (Fr. accointer, Lat. accognit- 
are, from cognosco, cognitus, to know), Apprise 
(Fr. appris, from apprendre, the Lat. appre- 
hendere ), and Advise ( Fr. aviser, Lat. ad and 
videre, visus, to see) closely resemble inform, 



OK TEACHING. 41 

inasmucli as they relate to the communication of 
matters of fact. I inform a man when I simply 
tell him a fact which he did not know before. 
I acquaint him with that of which I furnish 
him with all the details. So I inform him of the 
fact, and acquaint him with the particulars of it. 
I apprise him of what particularly concerns him 
to know, whether it be a good or an evil, or a 
danger, or a probability of any sort. I advise 
him of that which I impart to him formally, 
officially, or as in duty bound, of what occurs in 
due course." (Smith, Syn. Discr.) 



IV. 

ON AUTHORITIES. 

31. " So in literature, men of establislied re- 
putation, of classical merit, and known veracity, 
are quoted as authorities in support of any 
position." (Crabb, Synonyms.) 

32. " Authority may come from superior 
knowledge or information, or from natural as 
well as social or professional relationship." 
(Smith, Synonyms Discriminated.) 

33. ''The Principle of Authority.— ' The 
principle of adopting the belief of others, on a 
matter of opinion, without reference to the par- 
ticular grounds on which the belief may rest.' 

" The Argument from Authority. — It is an 
argument for the truth of an opinion that it has 
been embraced by all men, in all ages, and in all 
nations. Quod semper , uhiqne^ et ah omni- 
huSi are the morks of universality, according to 
Vincentius Lirinensis. ' This word is sometimes 
employed in its primary sense, when we refer to 
any one's example, testimony, or judgment ; as 
when, e.g., we speak of correcting a reading in 
some book on the authority of an ancient MS., 
or giving a statement of some fact on the author- 
ity of such and such historians, etc. In this 



OK AUTHORITIES. 43 

sense the word answers pretty nearly to the Lat- 
in auctoritas. It is a claim to deference. Some- 
times, again, it is employed as equivalent to 
potestas, power, as when we speak of the 
authority of a magistrate. This is a claim to 
obedience. ' 

" Consent. — 'Believing in the prophets and 
evangelists with a calm and settled faith, with 
that consent of the will, and heart, and under- 
standing, which constitutes religious belief, I 
find in them the clear annunciation of the king- 
dom of God upon earth. ' 

" Assent is the consequence of a conviction 
of the understanding. Consent arises from the 
state of the disposition and the will. The one 
accepts what is true ; the other embraces it as 
true and good and worthy of all acceptation. . . . 

"•'These things are to be regarded as first 
truths, the credit of which is not derived from 
other truths, but is inherent in themselves. As 
for probable truths, they are such as are admitted 
by all men, or by the generality of men^ or by 
wise men ; and among these last, either by all 
the wise, or by the generality of the wise, or by 
such of the wise as are of the highest authority.' 

" Assent is that act of the mind by which we 
accept as true a proposition, a perception, or an 
idea. It is a necessary part of judgment ; for if 
you take away from judgment affirmation or de- 
nial, nothing remains but a simple conception 
without logical value, or a proposition which 
must be examined before it can be admitted. It 
is also implied in perception, which would 



44 0^ AUTHORITIES. 

otherwise be a mere phenomenon wliicli the mind 
had not accepted as true. 

' ' Assent is free when it is not the unavoidable 
result of evidence, necessary when I cannot 
withhold it without contradicting myself. The 
Stoics, while they admitted that most of our 
ideas came from without, thought that images 
purely sensible could not be converted into real 
cognitions without a spontaneous act of the 
mind, which is just assent or beHef. 
'Assent of the mind to truth is, in all cases, the 
work not of the tmderstanditu/i but of the 
reason. Men are not convinced by syllogisms ;- 
but when they believe a principle, or wish to be- 
lieve, then syllogisms are brought in to prove it.* 

"Belief. — 'Belief, assent, conviction, are 
words which I do not think admit of logical defi- 
nition, because the operation of mind signified by 
them is perfectly simple, and of its own kind. 
Belief must have an object. For he who believes 
must believe something, and that which he be- 
lieves is the object of his belief. Belief is always 
expressed in language by a proposition wherein 
something is affirmed or denied. Belief admits 
of all degrees, from the slightest suspicion to the 
fullest assurance. There are many operations of 
mind of which it is an essential ingredient, as 
consciousness, perception, remembrance. We 
give the name of evidence to whatever is a 
ground of belief. AVhat this evidence is, is more 
easily felt than described. The common occa- 
sions of life lead us to distinguish evidence into 
different kinds ; such as the evidence of sense, 



O:^ AUTHORITIES. 45 

of memory, of consciousness, of testimony, of 
axioms, and of reasoning. I am not able to find 
any common nature to which they may all be 
reduced. They seem to me to agree only in this, 
that they are all fitted by nature to produce 
belief in the human mind, some of them in the 
highest degree, which we call certainty, others in 
various degrees according to circumstances. ' 

' ' St. Austin accurately says, ' We know what 
rests upon reason ; we believe what rests upon 
authority. ' The original data of reason do not 
rest upon reason, but are necessarily accepted 
by reason on the authority of what is beyond 
itself. These data are, therefore, in rigid pro- 
priety, beliefs or trusts. Thus it is, that in the 
last resort, we must, perforce, philosophically 
admit, that belief is the primary condition of rea- 
son, and not reason the ultimate ground of belief. 
We are compelled to surrender the proud Intel- 
lige ut credas of Abelard, to content ourselves 
with the humble Crede ut intelligas of Anselm. 

" To believe is to admit a thing as true, on 
grounds sufficient, subjectively; insufiicient, 
objectively. The word believing has been 
variously and loosely emplo}»ed. It is frequently 
used to denote states of consciousness which 
have already their separate and appropriate ap- 
pellations. Thus it is sometimes said, I believe 
in my own existence and the existence of an ex- 
ternal world, I believe in the facts of nature, 
the axioms of geometry, the affections of my 
own mind, as well as, I believe in the testimony 



46 OK AUTHOEITIES. 

of witnesses, or in the evidence of historical 
documents. 

" Setting aside this loose application of the 
term, I propose to confine it, first, to the effect 
on the mind of the premises in what is termed 
probable reasoning, or what I have named con- 
tingent reasoning — in a word, the premises of all 
reasoning, but that which is demonstrative ; and, 
secondly, to the state of holding true when that 
state, far from being the effect of any premises 
discerned by the mind, is dissociated from all 
evidence. I propose to restrict the term belief 
to the assent to propositions, and demarcate it 
from those inferences v/hich are made in the 
presence of objects and have reference to them. 
I would say, we believe in the proposition ' Fire 
burns, ' but know the fact that the paper about 
to be thrust into the flame will ignite." (Flem- 
ing, Vocab. of Phil.) 

34. " Another error is a conceit that of for- 
mer opinions or sects after variety and examina- 
tion the best hath still prevailed and suppressed 
the rest ; so as if a man should begin the labour 
of a new search, he were but like to light upon 
somewhat formerly rejected, and by rejection 
brought into oblivion : as if the multitude, or 
the wisest for the multitude's sake, were not 
ready to give passage rather to that which is 
popular and superficial, than to that which is 
substantial and profound ; for the truth is, that 
time seemeth to be of the nature of a river or 
stream, which carrieth down to us that which is 



ON" AUTHOEITIES. 47 

light and blown up, and sinketh and drowneth 
that which is weighty and solid 

** Another error hath proceeded from too 
great a reverence, and a kind of adoration of the 
mind and understanding of man ; by means 
whereof, men have withdrawn themselves too 
much from the contemplation of nature, and the 
observations of experience, and have tumbled 
up and down in their own reason and conceits. 
Upon these intellectualists, which are notwith- 
standing commonly taken f )r the most sublime 
and divine philosophers, Heraclitus gave a just 
censure, saying. Men sought truth in their own 
little worlds, and not in the great and com- 
mon world; for they disdain to spell, and so 
by degrees to read in the volume of God's 
works : and contrariwise by continual meditation 
and agitation of wit do urge and as it were in- 
vocate their own spirits to divine and give oracles 
unto them, whereby they are deservedly deluded. 

"Another error that hath some connexion with 
this latter is, that men have used to infect their 
meditations, opinions, and doctrines, with some 
conceits which they have most admired, or some 
sciences which they have most applied; and given 
all things else a tincture according to them, utter- 
ly untrue and improper. So hath Plato inter- 
mingled his philosophy with theology, and 
Aristotle with logic ; and the second school of 
Plato, Proclus and the rest, with the mathematics. 
For these were the arts which had a kind ol 
primogeniture with them severally. So have the 
alchymists made a philosophy out of a few ex- 



48 OK AUTHOKITIES. 

periments of the furnace ; and Gilbertus our 
countryman hath made a philosophy out of the 
observations of a loadstone. So Cicero, when, 
reciting the several opinions of the nature of the 
soul, he found a musician that held the soul was 
but a harmony, saith pleasantly. Hie ab arte sua 
non recessit, etc. But of these conceits Aristotle 
speaketh seriously and wisely when he saith, Qui 
respiciunt ad pauca de facili pronunciant. 

" Another error is an impatience of doubt, 
and haste to assertion without due and mature 
suspension of judgment. For the two ways of 
contemplation are not unlike the two ways of 
action commonly spoken of by the ancients : the 
one plain and smooth in the beginning, and in 
the end impassable ; the other rough and trouble- 
some in the entrance, but after a while fair and 
even : sd it is in contemplation ; if a man will 
begin with certainties, he shall end in doubts ; 
but if he will be content to begin with doubts, 
he shall end in certainties. 

*' Another error is in the manner of the tra- 
dition and delivery of knowledge, which is for 
the most part magistral and peremptory, and not 
ingenuous and faithful ; in a sort as may be soon- 
est believed, and not easiliest examined. It is 
true that in compendious treatises for practice 
that form is not to be disallowed : but in the 
true handling of knowledge, men ought not to 
fall either on the one side into the vein of 
Velleius the Epicurean, Nil tarn metuens, quam 
ne dubitare aliqua de re videretur ; nor on the 
other side into Socrates his ironical doubting of 



OK AUTHOEITIES. 49 

all things ; but to propound things sincerely 
with more or less asseveration, as they stand in a 
man's own judgment proved more or less. 

" Other errors there are in the scope that men 
propound to themselves, whereunto they bend 
their endeavours ; for whereas the more constant 
and devote kind of professors of any science 
ought to propound to themselves to make some 
additions to their science, they convert their 
labors to aspire to certain second prizes : as to 
be a profound interpreter or commenter, to be a 
sharp champion or defender, to be a methodical 
compounder or abridger, and so the patrimony 
of knowledge cometh to be sometimes improved, 
but seldom augmented. 

" But the greatest error of all the rest is the 
mistaking or misplacing of the last or furthest 
end of knowledge. For men have entered into 
a desire of learning and knowledge, sometimes 
upon a natural curiosity and inquisitive appetite ; 
sometimes to entertain their minds with variety 
and delight ; sometimes for ornament and repu- 
tation ; and sometimes to enable them to victory 
of wit and contradiction ; and most times for 
lucre and profession ; and seldom sincerely to 
give a true account of their gift of reason, to 
the benefit and use of men : as if there were 
sought in knowledge a couch whereupon to rest 
a searching and restless spirit ; or a terrace for 
a wandering and variable mind to walk up and 
down with a fair prospect ; or a tower of state, 
for a proud mind to raise itself upon ; or a fort 
or commanding ground, for strife and conten- 



50 ON AUTHORITIES. 

tion ; or a shop, for profit or sale ; and not a 
rich storehouse for the glory of the Creator and 
the relief of man's estate. But this is that which 
will indeed dignify and exalt knowledge, if con- 
templation and action may be more nearly and 
straitly conjoined and united together than they 
have been ; a conjunction like unto that of the 
two highest planets, Saturn, the planet of rest 
and contemplation, and Jupiter, the planet of 
civil society and action. Ilowbeit, I do not mean, 
when I speak of use and action, that end before- 
mentioned of the applying of knowledge to lucre 
and profession; for I am not ignorant how much 
that diverteth and interrupteth the prosecution 
and advancement of knowledge, like unto the 
golden ball thrown before Atalanta, which while 
she goeth aside and stoopeth to take up, the 

race is hindered 

" Neither is my meaning, as w^as spoken of 
Socrates, to call philosophy down from heaven 
to converse upon the earth ; that is, to leave 
natural philosophy aside, and to apply knowl- 
edge only to manners and policy. I3ut as both 
heaven and earth do conspire and contribute to 
the use and benefit of man ; so the end ought to 
be, from both philosophies to separate and reject 
vain speculations, and whatsoever is empty and 
void, and to preserve and augment whatsoever is 
solid and fruitful." (Bacon, Advancement of 
Learning, pp. 39-43, ed. 1868.) 



EECAPITULATIOX. 

35. This brief Introductory Discussion, re- 
capitulated, exhibits the following synopsis : 

I. Pedagogics includes — 

1. Education, 

2. Ethics, 

3. Psychology. 

II. Education rests upon materials con- 
tained WITHIN — 

1. Ethics, 

2. Psychology. 

III. Education, in part, depends upon — 

1. Teaching. 

IV. Teaching assumes a knowledge of the 

TWO ELEMENTS — 

1. The mind that is to be taught— 

Psychology, 

2. The subject-matter that is to be 

learned, drawn from — 

{a) Ethics, 

(&) Psychology. 
V. On Authorities. 



PART SECOND. 



§§ 36-57. 

ON METHOD IN GENERAL. 



Method, . 

System, 

Analysis, 

Separation, 

Synthesis, 

Definition, 

Abstraction, . 

Reconstruction, 

Generalization, 

Classification, . 

Induction, 

Interpretation, 

Repetition, . 

Deduction, 

Manner, . 

Mode, . 



§§ 36-9. 

§41. 
. §43. 

§44. 
. § 45. 



§46 

§ 47. 



§ 49. 
§ 50. 
§51. 
§53. 



§ 53. 
§54. 



§ 55. 
§56. 

§57. 



ON METHOD IN GENERAL. 

36. Method signifies literally tlie ivay to 
seek after a thing. The Greek philosophers used 
the word in this general sense, which has been 
retained to the present. Although writers agree 
substantially in assigning to the term the notion 
of Avay, a principle which determines direction, 
or orderly arrangement, yet the precise limita- 
tions of the way are not attributed with equal 
clearness and uniformity. By some, the term 
implies the only way in which a thing can be 
done. By others. Method is the only philosophi- 
cal way of proceeding in an investigation, in- 
volving actually two operations, analysis and 
synthesis. Still others see in the word only a 
particular way of doing a given thing, which way 
may or may not depend upon the individuality 
of those who achieve the task. (See Appendix 
A, § 225.) 

37. Method in general never has respect to 
the mind of the learner, but always has reference 
to the subject studied. It assumes intellectual 
activities and products. It is simply the way in 
which the mental products are utilized and 
unified into science. This field is that of logic. 
" I adopt the opinion of Mr. Herbert Spencer, 
that logic is really an objective science, like 



56 ON^ METHOD IIS" GEIS'ERAL. 

mathematics or meclianics." (Jevons, Pri. 
Sci., p. 4, ed. 1877.) 

38. The conception of Method resting upon 
substantial data at either end of the process, it 
is within the province of the term to speak of 
methods of business, when referring to this or 
that general way by which business transactions 
are accomplished. (See Appendix A, § 225.) 

39. " The result has been half a century of 
steady and unprecedented material growth, ac- 
companied with corresponding improvement in 
the structure of Government, which is probably 
unequalled to-day in the success with which 
scientific methods are made to work through 
popular forms." {The Nation, No. 700, p. 328, 
November 28, 1878.) *' In a commercial country, 
which depends so much on the maintenance of 
credit, nothing is so important as that the credit 
should rest on solid foundations — not merely that 
the bases of the several transactions should be 
secure, but that the methods of business should 
be regular, legitimate, and trustworthy. The 
credit of an individual and of a bank depends 
much more on the known fact that the business 
done is done in a regular way, and with the 
habitual observance of certain rules of safe con- 
duct, than upon a knowledge of the particular 
securities which accompany it. The one fact 
should be certified to the public in all possible 
ways, the other is in its nature private. {Ibid,, 
p. 330.) 

40. In any investigation three distinct elements 
are presented to the inquirer : (1) The object- 



01^ METHOD IK GEITERAL. 57 

matter, whicli is tlie end of tlie inquiry ; (2) 
The way in which the activities of the examiner 
move forth and continue, while arriving at the 
end ;' (3) The state or condition of the one who 
is putting forth the exertion to secure the end. 
A direct discussion suggests these questions : 
(1) Does Method regard immediately and solely 
the object-matter of the investigation, how it is 
finally left, or to be left, by the student, whether or 
not it shall be in an orderly arrangement, as 
of Classification ? (2) Or does it regard only 
the way in which the inquiry proceeds, as by An- 
alysis, Synthesis, Induction, Deduction, Classifi- 
cation, or Generalization ? (3) Or does it con- 
sider especially the way in which the scholar, as 
as a particular individual, carries on his work, 
whether in this or that state of mind or body, 
or by means of these or those carefully chosen 
and utilized expedients and appliances which are 
peculiar to himself alone ? 

That is, in recapitulation : (1) Does Method 
point sharply and first to the object investigated, 
in what shape, form, or condition it shall be 
left ? (2) Or does it indicate the direction, or 
way in, or over, which the energy of the mind 
moves in its activity ? (3) Or does it judge the 
characteristics which are the difference between 
the mind of the examiner and that of other men ? 
In order to answer these questions, it becomes 
necessary to attend to each in turn. 

41. I. Consider the object-matter of study, 
whatever it may be, as arithmetic, botany, or 
grammar. The purposes of examining any ob- 



58 OK METHOD IK GEKERAL. 

ject are to know it ; to apprehend its parts, as 
single things ; to discover the relations which 
exist among those parts ; to rearrange its parts 
and relations, if thereby the mind can better 
seize, comprehend, or remember them, singly 
and collectively ; to classify these parts into 
some new whole, which is the product solely of 
intellectual activitj^ called thought, reflection, or 
simply reason. The student finds the object- 
matter of his attention in an apparently hetero- 
geneous mass of disorder and confusion — he 
leaves it reduced into a congruous condition — he 
has been entirely unconscious of his own eccen- 
tricities, or individuality, or expedients, or ways 
in which his activities and energies have pro- 
ceeded, whether by this or by that process or 
route — he has steadfastly and daily kept his at- 
tention upon the object-matter, as to what it is, 
and how he shall finally leave it adjusted, part 
to part, part to the whole, and the whole to 
other parts and wholes — himself and the ways 
by which his thought-powers went along in their 
work have dropped entirely out of consideration. 
In this case the idea of searching out is not 
found, because the attention rests exclusively 
upon the object-matter which incited and de- 
termined the action called seeking after — that 
is, the student considers the purposes attained, 
and not the routes or ways through or by which 
his powers brought forth those classified and 
organized ends. It follows, hence, that this is 
not a case of Method. The result or end spoken 



OK METHOD IN" GENERAL. 59 

of is properly a system, economy, or constitu- 
tion. (See § 124, and Appendix B, § 226.) 

42. II. Consider exclusively the ways over 
which the activities of the intellect proceed when 
they are engaged in an investigation. These may 
be called Modes of Method in General. 

43. (o) The faculties of observation are on 
the alert to discriminate the parts of the wholes 
of the object -matter of investigation, and the at- 
tributes or characteristics of those parts or wholes 
— these parts and attributes are likewise observed 
under the light of thought or reflection, called 
comparison, by which the analogous elements of 
similars are discovered. This way, by which the 
powers of the mind must pass in order to discover 
the individual Facts, known as elements, for the 
relations called similars and dissimilars, is prop- 
erly denominated Analysis. (See Appendix C, 

§22^-) . . ... 

44. A rigid distinction should be observed 

between analysis and separation, or division. 

Separation sets apart one thing from another — tbe 
thing set aside may be a part of that from which 
it is now placed, or it may be some other Avhole 
thing placed apart from the former. Division 
implies a taking asunder, and ordinarily refers 
to some whole which is cut into parts. In separa- 
tion or division the process ends with the action, 
while in analysis these parts are not only made or 
found, but they are examined for the purpose of 
discovering similarities. Separation and division, 
having set apart the portions, give them no farther 
examination nor attention. An artisan takes a 



60 01!^ METHOD i:n' gejteral. 

watcli into its parts for the purpose of cleaning 
and repairing the time-piece. His examinationof 
each part is to the sole end of discovering whatever 
particles of dust may be adhering to it. There is 
no examination in the interests of science or 
higher truth, either theoretical or practical. This 
is a case of separation, rather than of analysis. 

45. (h) Assuming the foregoing analysis com- 
plete, the powers of thought apprehend the 
elements, which are to constitute the similars, 
and from them create a new intellectual product. 
In this process the unassimilative elements are 
rejected by the mind, and form no portion of the 
new products. The way or route by which the 
mind proceeds in creating these intellectual pro- 
ducts is called Synthesis. (See Appendix D, 
§228.) 

46. Sometimes the elements of a synthesis 
are the products of Befinition. (See Appendix 
E, § 229.) 

47. The process of assorting and rejecting 
the analytical elements is known as Abstraction. 
(See Appendix F, § 230.) 

48. " Analysis and synthesis, though com- 
monly treated as two different methods, are, if 
properly understood, only the two necessary 
parts of the same method. Each is the relative 
and the correlative of the other. Analysis, with- 
out a subsequent synthesis, is incomplete ; it is 
a mean cut ofE from its end. Synthesis, without 
a previous analysis, is baseless ; for synthesis 
receives from analysis the elements which it re- 



OK METHOD IN GENEEAL. 61 

composes/* (Sir W. Hamilton, Metaphysics, 
p. 69, ed. 1871, Boston.) 

49. Sjmthesis should be discriminated from 
Reconstruction — it is Construction. Recon- 
struction is the opposite of separation or division ; 
it simply re-makes the whole by re-adjusting those 
elements or parts which were set aside from each 
other — it fashions no new whole. Synthesis is 
Construction ; it fabricates an original product 
which essentially and materially differs in its 
nature from any and all of the wholes that were 
separated by analysis. In the supposition of the 
watch (§ 44), if the parts be restored to their 
former position, and the watch * ' put together ' ' 
again, it is a case of reconstruction, rather than 
of synthesis. There is no new product created 
by the procedure. 

50. (c) Analogous elements being assumed 
in the possession of the student, he proceeds by 
synthesis to " comprehend, under a common 
name, several objects agreeing in some point 
which he abstracts from each of them, and which 
that common name serves to indicate." This 
way of proceeding is usually known under the 
name of Generalization. (See Appendix G, 
§231.) 

51. {d) Generalization, in its ways of pro- 
ceeding, is but another name for classification, 
although in the extent to which they are carried 
in science classification is the more comprehen- 
sive term. By some writers, generalization is 
used in reference to the object-matter of cause 
and effect, while investigation proceeding on the 



62 OK METHOD IK GENERAL. 

idea of observed resemblances, is the province of 
Classification. (See Apj)endix //, § 232.) • 

52. (e) When generalization or classification 
is complete in extension at any point in the 
ascending degrees, and the scholar, by his powers 
of thought, extends the generalization by infer- 
ence so as to include objects which the preced- 
ing generalization does not cover in his experience 
or observation — thus making a new creation, 
known as a universal, sometimes as a general — 
the product is called an Induction. (See Ap- 
pendix I, § 233.) 

53. Induction should not be confounded with 
pure explanation, or what is known as Mathe- 
Tnatical Interpretation, Induction creates a 
new inferential product, the elements of which are 
discovered only by the examination of many ob- 
jects, and the inference extends over unexamined 
and unexplored territory. Interpretation places 
itself at the point of completion of a single 
observation, operation, or process, and retraces 
the steps over the way followed, and explains 
fully the meaning, extensive and intensive, of 
what is observed, predicting simply that all similar 
examples will be traced along the same way, and 
the same ends reached. Sciences founded upon 
general definitions instead of observation and ex- 
periment, are not inductive. The Pure Mathe- 
matical sciences are not properly inductive, and 
from their nature cannot be. What is usually 
called Mathematical Induction is Interpretation. 
The so-called Perfect Induction is hardly Induc- 
tion in its nature, because no product is created 



OK METHOD IK GEKEKAL. 63 

beyond a generalization, or classification, and 
nothing is gained by using two terms for the 
same thing, when there are two notions to be 
distinguished from each other. (See Appendix 
ly § 233, Nos. 4, 5, and 7. Also Appendix J, 
§234.) 

54. Another point should be clearly outlined : 
The mere Repetition of examples, substantially 
identical, does not increase the force and certi- 
tude, nor extend the range, of an inference. One 
example covers the whole territory, and it, to- 
gether with all others of the kind, does no more 
than illustrate the original principle established 
directly or indirectly by definition. In arith- 
metic, for example, repetition of examples adds 
nothing to the elements of which the " rule" 
is made — it simply serves to impress the way, 
the procedure, upon the mind of a learner, simi- 
larly to the repetition in the finger exercises 
upon the piano. (See §§ 204-7.) 

It should be observed that there is a great 
variety of opinions among authors concerning the 
nature of Induction. The citations in the Ap- 
pendix exhibit some of the views. 

55. (/) If a scholar assume the possession of 
generals or universals, furnished either by In- 
duction, by Definition, or by Intuition, and then 
use them with which to compare individual facts 
or truths, and by this means establish individual 
truths of like kind as an end of the process, the 
way of proceeding is known as Deduction. (See 
A2opendix K, § 235.) 

56. III. Consider the way in which the 



64 OK METHOD IK GENERAL. 

individual student addresses himself to his tasks. 
He may be proceeding by any of the above- 
named modes, or ways, usually called Methods, 
and his own characteristics of disposition, habits, 
eccentricities, may be prominent. These may or 
may not be aids in securing valuable results of 
his labors. In any case, these are simply and 
solely individualities — they belong exclusively to 
the investigator — they are no necessary part of 
the mode or Method he is following — they are 
his Manner. 

Critical discrimination should be made be- 
tween what is necessary to a way, and what is 
purely incidental to the individual who is pro- 
ceeding over that way. Indifference to this 
discrimination is followed by the pedantic asser- 
tion that each man can have a method of his 
own. Methods are ways which are independent 
of this or that man, and which are determined 
by the nature of the mind of man, or by the 
nature of the object-matter to be investigated. 
But Manner is his individuality when proceeding 
in a Method. (See § 123.) 

57. When one's Manner is well ordered in its 
System, it is designated by the term Mode. (See 
§ 123.) 



PART THIRD. 

§§ 58-216. 

ON METHODS OF TEACHING. 



I. On the Theory of Methods 

OP Teaching, ....§§ 58-143 

II. On the Practice of Methods 

OF Teaching, ....§§ 144-216 

(A) On the Knowing Faculties 

'', of the Mind, ....§§ 144-187 

(B) On the Nature of Subject- 
Matter, §§ 188-210 

(C) On Discovering Methods of 
Teaching Special Subjects, . §§ 211-216 

III. Concluding Reflections, . §§ 217-224 



I. 



ON THE THEORY OF METHODS OF 
TEACHING. 

58. " I am afraid it must be allowed, that no 
art, of equal importance to mankind, lias been 
so little investigated scientifically as the art of 
teaching. No art is in the hands of practition- 
ers who are so apt to follow so blindly in the old 
paths. I say this with the full recollection that 
there has been great improvement in England 
lately, and that the books of teaching, most in 
use, have been purged of many gross errors both 
of statement and of method. But one line of 
enquiry there is which has never been sufficiently 
followed, though one would have thought it ante- 
cedently the most promising of all, — the study of 
the human mind through actual observation, and 
the study of the expedients by which its capacity 
for receiving and retaining knowledge may be en- 
larged. The field of investigation has been al- 
most wholly neglected, and therefore it may just 
be that we are on the eve of great discoveries in 
education, and that the processes of these teach- 
ers are only a rough anticipation of the future. 
The fact that the methods of teaching follow- 
ed in England are almost wholly empirical, that 



68 01^ THE THEORY OF 

for the most part tliey entirely neglect individual 
differences of character and temperament, that 
they certainly work counter to the known laws 
according to which some of the mental faculties 
operate, — for example, the memory — all these 
facts seem to my mind to point at possibilities 
and chances of improvement, which a few 
persons, by expedients which, I frankly allov/, 
seem even to me somewhat ignoble, have perhaps 
had the good fortune to realize beforehand." 
(Maine, Village Communities and Miscellanies, 
ed. 1876, pp. 285, 286.) 

59. A complete discussion of the Theory of 
Methods of Teaching would include a full inves- 
tigation of Psychology and of the nature of sub- 
ject-matter to be taught — it would be an exhaus- 
tive examination of the relations which exist be- 
tween the various faculties of the mind and the 
many kinds of objects to be learned. It would 
inquire, first, how mind acts as an original cause 
of activity, then what are the nature and char- 
acter of its capacities, and lastly what are the 
products of its activity. This investigation is 
purely psychological, and lies anterior to the 
province of logic — it is supra-logical, and regards 
the function, nature, and character of the activi- 
ties and faculties of the mind that learns, and 
that grows by introsusception. 

60. By the nature of a faculty is meant not 
only its function, but that native endowment of 
its Potentiality out of which grow all those suc- 
cessive degrees of power that manifest themselves 
in a reality. ^ 



METHODS OF TEACHING. 69 

61. By the character of a faculty is designat- 
ed the state in which it exists at any specified 
stage in its growth. 

62. By Psychology is meant the introspective 
study of the experience of the mind itself. 

63. "No student of Locke and Hume can 
read the psychological works of the present day 
without feeling anxiety for the future of the study 
of Mind or Experience. The modern psycholo- 
gist is profoundly dissatisfied with his subject ; 
the exact and the classificatory sciences, by the 
brilliance of their methods and results, fill him 
with envy ; he is painfully conscious that mental 
phenomena are not definite enough to be the ob- 
jects of a science ; he must therefore connect 
them with other phenomena which are. Hence 
the ' Physiological Psychology ' of our day. But 
surely this is not psychology, or the study of ex- 
perience, but physiology. Let us keep clearly 
before our minds that psychology is the study 

of experience Psychology then, if we 

retain the word, is a critique, a Method, a 
certain thoughtful attitude in science, morals, and 
literature. It is the critical examination of my 
own adult opinions, desires and tastes in rela- 
tion to present objects No amount 

of information respecting the evolution of belief 
or sentiment, and no amount of mental physiol- 
ogy can ever take the place of acquaintance with 
my own real opinions and desires. Modern works 
on mental science, with very few exceptions, 
forget this. The conditions of ideation, the 
origin of moral and aesthetic feelings, and such 



70 ON THE THEORY OF 

like, are fully discussed ; but we look in vain 
for a home-question like this — ' After all, do I 
really desire nothing for myself but Ha^^piness. ' 
Individualism — thoughtful reference to one's 
own experience — is indeed a rare quality now." 
(Stewart, Psychology, in Mind, pp. 445-451, 
No. IV, October, 1876.) 

64. Methods of Teaching, having an ac- 
quaintance with Mind, consider the nature of 
intellectual products, show in what order they 
follow each other, reveal the way in which the 
activities of Mind proceed with these products, 
classify them, and build up Science out of them. 
This is the arena of Logic, and has reference to 
System, or subject-matter as such — it is infra- 
psychological. Succeeding this comes a thorough 
discussion of subject-matter that is to be learned 
by the mind of the student. A treatment so 
elaborate could not be concluded in one brief 
Study, were it desirable to attempt it. Another 
occasion must serve portions of this work, as it 
may occur. No more will be essayed at this 
time than to survey the line of the investigation 
as well as may be, by " blazing" the way, some- 
times " doublingupon the track," so that others 
may follow and clear np the obscurities and re- 
move the errors, that lie upon this intricate 
way, and enlarge the practical value which must 
result from a scientific research. 

65. " Since the human mind must conscious- 
ly reproduce what actually exists, the act of 
knowing is conditioned in two ways : a. Sub- 
jectively, by the essence and natural laws of the 



METHODS OF TEACHIKG. 71 

human mind, especially by those of the hmnan 
powers of knowledge ; b. Objectively, by the 
nature of what is to be known. The constitu- 
tions and relations of what is to be known, so far 
as these require different ways of representation 
in the act of knowing, we call forms of existence 
{e.g., subsistence and inherence). The notions 
of these forms of existence are the metaphysical 
categories. The different ways, corresponding 
to these forms of existence, in which what actual- 
ly exists is taken hold of and copied in the act 
of knowledge, are the forms of knowledge {e.g., 
the categorical judgment). The actual copy, the 
result of the activity of knowledge, is the con- 
tent of knowledge. . . . The laws of 
knowing, as such, determine only the ways of 
representation (copying), or the forms of knowl- 
edge, not its contents. . . . These forms 
of knowledge correspond to the forms of exist- 
ence, and they are conditioned by the objective 
reality." (Ueberweg, Log. Doct., pp. 3, 4, ed. 
1871.) 

6S. " The sense attached at the present day 
to the words form and matter, is somewhat dif- 
ferent from, though closely related to, these 
(form and law). The form is what the mind 
impresses upon its perceptions of objects, which 
are the matter ; form therefore means mode of 
viewing objects that are presented to the mind. 
When the attention is directed to any object, 
we do not see the object itself, but contemplate 
it in the light of our own prior conceptions. A 
rich man, for example, is regarded by the poor 



72 ON THE THEORY OF 

and ignorant under tlie form of a very fortunate 
person, able to purchase luxuries which are 
above their own reach ; by the religious mind 
under the form of a person with more than or- 
dinary temptations to contend with ; by the 
political economist, under that of an example of 
the unequal distribution of wealth ; by the trades- 
man, under that of one whose patronage is 
valuable. Now, the object is really the same to 
all these observers ; the same rich man has been 
represented under all the different forms. And 
the reason that the observers are able to find 
many in one, is that they connect him severally 
with tlieir own prior conceptions. The form, 
then, in this view, is mode of knowing ; and 
the matter is the perception, or object, we have 
to know." (Thompson, Outline of Laws of 
Thought, p. 34, 2d ed.) 

67. ^' Form is something which may remain 
uniform and unaltered, while the matter thrown 
into that form may be varied. Medals struck 
from the same dies have exactly the same form, 
but they may be of various matter, as bronze, 
copper, gold, or silver. A building of exactly 
the same form might be constructed either of 
stone or bricks ; furniture of exactly similar 
shape may be made of oak, mahogany, walnut 
wood, etc." (Jevons, El. Les. Logic, ed. 1878, 
pp. 4-5.) 

68. " Distinction between Form and Mat- 
ter. — This phraseology was introduced by Aris- 
totle, who represented every thing as having in 
itself both matter and form. It had a new 



METHODS OF TEACHING. 73 

signification given to it by Kant, who supposes 
that the mind supplies from its own furniture a 
form to impose on the matter presented from with- 
out. The form corresponds to the a priori ele- 
ment, and the matter to the a posteriori. But 
the view thus given of the relation in which the 
knowing mind stands to the known object is 
altogether a mistaken one. It supposes that the 
mind in cognition adds an element from its own 
resources, whereas it is simply so constituted as 
to know what is in the object. This doctrine 
needs only to be carried out consequentially to sap 
the foundations of all knowledge, — for if the 
mind may contribute from its own stores one 
element, why not another ? Why not all the 
elements ? In fact, Kant did, by this distinction, 
open the way to all those later speculations 
which represent the whole universe of being as 
an ideal construction. There can, I think, be 
no impropriety in speaking of the original prin- 
ciples of the mind as forms or rules, but they 
are forms merely, as are the rules of grammar, 
which do not add any thing to correct speaking 
and writing, but are merely the expression of the 
laws which they follow. As to the word ' mat- 
ter,' it has either no meaning in such an appli- 
cation, or a meaning of a misleading character." 
(McCosh, Int. of Mind, p. 312, ed. 1870.) 

69. " The drift and meaning of a branch of 
knowledge varies with the company in which it 
is introduced to the student. If his reading is 
confined simply to one subject, however such 
division of labor may favor the advancement of a 



74 OIT THE THEORY OF 

particular pursuit, a point into wliicli I do not here 
enter, certainly it has a tendency to contract his 
mind. If it is incorporated with others, it de- 
pends on these others as to the kind of influnce 
which it exerts upon him. Thus the Classics, 
which in En2:land are the means of retinino; the 
taste, have in France subserved the spread of re- 
volutionary and deistical doctrines. In Meta- 
physics, again, Butler's Analogy of Religion, 
which has had so much to do with the conversion 
to the Catholic faith of members of the Univer- 
sity of Oxford, appeared to Pitt and others, who 
had received a different training, to operate only 
in the direction of infidelity. . . It is not so 
much this study or that, as it is the setting into 
other studies that moulds the impression. In 
this is the notion of being liberally educated — 
that any subject is received without prejudice." 
(Newman, Idea of A University, p. 100, ed. 
1873.) 

70. " The policy of the present Minister of 
Public Instruction (Russia) has been to discoun- 
tenance the study of natural science, as the source 
of mutiny and insubordination, and encourage 
that of the classics, as favorable to discipline 
and authority and to the state of religion." 
{TheJVation,^^o. V04, Dec. 26, 1878, p. 393.) 

" The generality of travellers enveloped for- 
ever in customs, habits, prejudices, and wants 
peculiar to themselves, move, as it were, in an 
atmosphere of their own, which divides them 
from the places through which they pass, as from 
so many different worlds. A Frenchman would 



METHODS OF TEACHING. 75 

fain carry all France along with liim ; as soon as 
he misses the smallest of his accustomed con- 
veniences, he overlooks its equivalent, and be- 
lieves himself lost. Comparing* continually 
what he sees with what he has quitted, he thinks 
it worse only because it is not the same, and 
cannot sleep in the Indies if his bed is not made 
as it was at Paris. ' ' (Rousseau, Emilius, vol. iv., 
pp. 226-7.) 

71. *^ Knoivledge is a general term which im- 
phes the thing known: science, learning, and 
erudition, are modes of knowledge qualilied by 
some collateral idea : science is a systematick 
species of knowledge which consists of rule and 
order ; learning is that species of knowledge 
which one derives from schools, or through the 
medium of personal instruction ; erudition is 
scholastick knowledge obtained by profound re- 
search ; knowledge admits of every possible de- 
gree, and is expressly opposed to ignorance ; sci- 
ence, learning, and erudition, are positively high 

degrees of knowledge Learning i^ 

less dependent on the genius, than on the will of 
the individual ; men of moderate talents have 
overcome the deficiencies of nature, by labour and 
perseverance, and have acquired such stores of 
learning as have raised them to a respectable 
station in the republick of letters. Profound eru- 
dition is obtained but by few ; a retentive mem- 
ory, patient industry, and deep penetration, are 
requisites for one who aspires to the title of an 
erudite m-dn.''^ (Crabb, Synonyms.) 

12t. All knowledge that we possess must be 



76 ON THE THEOKY -OF 

in some form — it would be well to say shape, if 
intellectual products or impressions could have 
shape. The term knowledge is sometimes used 
in two meanings : as completed thought, which 
is a product ; and as the action of the mind, the 
completion of which is a product. There is 
greater philosophical precision if the term be 
assigned only one signification — that of the 
noun, act or product. " Knowledge in its ex- 
actest definition is, in its positive form, A Con- 
scious identification of Attribute with its sub- 
ject, as in the affirmative proposition, the sun is 
bright. In its negative form, it is A Conscious 
differencing of an Attribute from its subject, 
as in the negative proposition, the sun is not 
dark." (Day, Outl. Ontolog. Science, p. 32, ed. 
1878.) 

73. " KnoAvledge is the act or product of a 
rational nature. As such it ever tends to a sys- 
tem which is characterized by singleness of 
source and aim ; and this tendency is along the 
line Avhich reason prescribes to a movement 
from a recognized source to the proposed end. 
There are different specific sources, as there are 
manifold specific aims in knowledge, indeed ; but 
reason is one and its field is one and its aim 
one, comprehensive of all special objects and all 
special aims. There is such a thing, therefore, 
as a method in all true rational knowledge." 
{Ihid., p. 31.) 

74. In these three distinct things — the source^ 
the etidf and the tvay of knowledge — the last is 
the method of knowledge. " The aim of knowl- 



METHODS OF teachi:n^g. 77 

edge is Truth. Knowledge arrived at the cer- 
tainty of truth is Science. Material (or real) 
truth must be distinguished from (formal) cor- 
rectness. Material truth in the absolute sense, 
or simply truth, is the agreement of the content 
(attributes) of knowledge with what actually 
exists. Material truth in the relative sense, or 
phenomenal truth, is the agreement of the me- 
diately acquired .content of thought with the im- 
mediate outer or inner perceptions which exist 
when the soundness of the mind and of the 
bodily organs is undisturbed, or would exist 
under the corresponding outer conditions." 
(Ueberweg, Logical Doct., pp. 5, 6, ed. 1871.) 

75. All these illustrations of the province of 
knowledge compel attention to the stages of the 
process of acquiring knowledge by the mind of 
the learner. (1) There is the source of the 
activity residing in the innate pov/er of the 
mind to act responsively and intuitively at the 
presence of objects to be known. This in- 
nate power of the mind is called the ultimate 
Cause of Knowledge, or simply the Cause. (2) 
There is the rational way in which this activity 
proceeds, usually at the dictation of the power 
of the Will. This way is known as the Method 
of Thought. (3) There is, lastly, the end of the 
activity. This consummation of the process into 
completeness is known as the act, or product of 
knowledge, or simply Knowledge. 

76. The preceding discussion relates, in the 
most general sense, to the consideration of 
knowledge as acquired by the learner. In or- 



78 Oiq- THE THEORY OF 

dinary acceptance the notion of learning is as- 
sociated with two persons — the one an instruc- 
tor or teacher of the other, who is called the 
learner, student, scholar, child, or pupil. When 
the pupil learns through the instrumentality of a 
living teacher he is said to be taught. 

77. When he learns without this instrumen- 
taUty, he is said to be self -in fortified, or self- 
ediicated. The self-informed student applies 
himself to understand whatever engages his atten- 
tion, whether books, or objects of nature, or works 
of art ; he applies his powers of observation and 
of reason to the things that he finds scattered 
about him as a heterogeneous mass ; he constructs 
his own questions for himself, invents his own 
illustrations, creates his own hypotheses, and ad- 
judges the validity of his own arguments and 
conclusions — that is, he alone pronounces upon 
the form and matter of his knowledge, and 
way of approaching it. In very many impor- 
tant matters he must leave it for time and experi- 
ence to inform him whether his knowledge is 
correct in fact. The element of time spent in 
arriving at truth by the self-educated student is 
often great for the amount and quality of knowl- 
edge gained. The difficulties that present them- 
selves to this learner are frequently sufficient to 
deter any but the most persevering and venture- 
some from attempting to surmount them. The 
fields of learning are so many and so extensive, 
and human life so short, that the imperative 
demands of our brief years give a practical 
value to some kinds of knowledge over others. 



METHODS OF TEACHING. 79 

The exclusively self-informed student is not as- 
sured that his learning is best calculated to pro- 
mote the welfare of himself and his fellow-man. 
A well-authenticated instance, related to the 
writer by Dr. J. Dorman Steele, will illustrate 
this statement : A young man of excellent 
parts entered college. He had adopted the 
theory that self-education is the only way to 
learning, and refused to consult or study books 
to prepare his lessons. He attended the recita- 
tions, observed closely what was said there, and 
depended upon his genius, or " inner conscious- 
ness," to evolve from himself the knowledge 
he possessed. In process of time he was grad- 
uated, and dropped into obscurity. After five 
or six years he suddenly appeared at the office 
of the president of the college. He desired to 
submit to the president a law in physics which 
he had discovered by his own unaided obser- 
vations during the past six years. If approved 
by the president, he would publish his discov- 
ery. He had discovered " that heat expands 
metals, and cold contracts them." The presi- 
dent called his little daughter, and asked her, 
what is the " first law in Natural Philosophy "? 
She said, " That heat expands metals, and cold 
contracts them." Said the president, " You 
see how many valuable years you have lost by 
neglecting to study books as well as objects, 
depending entirely upon your own inner con- 
sciousness for your knowledge. ' ' 

78. These considerations of reason and ex- 
perience bring forward the idea of aiding the 



80 OK THE THEORY OF 

youth of the State by means of appropriating 
to their benefit the learning and experience of 
some of the older members of the State. Those 
who consciously and methodically aid the young 
in acquiring learning and experience are known 
as Teachers, The efforts, which they put forth 
to advance their pupils in knowledge, constitute 
the idea that is designated Teaching. 

79. Teaching is consciously adjusting ob- 
jects and acts to the proper faculties and ca- 
pacities of the learner. ^''Adjust is to set right 
(Fr. juste, straight, right). Hence the word 
implies some relative order, shape, or standard, 
to which matters have to be brought, or some 
antecedent condition of inherent fitness to 
which they have to be reduced." (Smith, Syn. 
Discr.) The order in which objects are to be 
presented to the pupil is determined by the 
teacher. Nature, as the child finds her, pre- 
sents objects to it in an unclassified, promis- 
cuous mass. The pupil may see a cat, then an 
elephant, then a thunder-storm, all in one hour. 
The teacher would present objects in a sequence 
determined by previous study and classification. 
This order is artificial to the child, compared 
to the heterogeneous order in which Nature ex- 
hibits objects to it. From this view, it may be 
said that teaching is the conscious and philo- 
sophic adjustment of object-matter to the abili- 
ties of the pupil. 

80. The teacher has other duties towards his 
pupil. He presents before the mind of the 
learner some entire object — Nature also usually 



METHODS OF TEACHIXG. 81 

does this, but she leaves the mind to struggle 
with the whole at once — the teacher, finding the 
whole too vast for the pupil, separates it, prac- 
tically and virtuahy, into parts. This process 
of dissection may be accomplished by using the 
scalpel, the hammer, or by questions ; for ques- 
tions are but knives that dissect out parts to 
display to the pupil, or they are colter-shares 
that cut out furrows in the turf, narrower or 
wider, for the pupil to turn over, according to 
his strength. 

81. The teacher has still other duties in the 
case. He is to note both the form and the 
matter of the knowledge which the learner 
acquires, whether it stand in his mind correct in 
its impression and true in its essence. To se- 
cure these ends requires consummate skill of the 
teacher : his reason must be well trained and 
certain in its logical processes, his wit must be 
ready at analogies, his imagination must be fer- 
tile in illustration, his hands must be cunning in 
constructing, his understanding must be pro- 
found, and his knowledge must be overflowing 
in its quantity. Here lie the purely professional 
regions of teaching — here also are the processes 
catled Methods of Teaching. 

82. The teacher has now reached the great 
question of the Profession : How to teach ? 
For it is in teaching and with teachers, as it is 
in Logic, " Where two conditions are found or 
assumed : Firstly, that there exist certain men- 
tal laws to which every sound thinker is bound 
to conform. Secondly, that it is possible to 



82 OK THE THEOKT OF 

transgress those laws, or to think unsoundly." 
(Mansel, Prolegomena Logica, p. 16, ed. 1860.) 

83. In order to answer this question. How 
to teach ? even approximately, it is necessary 
to enter into a more critical examination of the 
conception of the word Teaching. To teach 
requires, obviously : (1) The mind of the 
learner, or the learner ; (2) The mind of the 
instructor, or the teacher ; (3) The objects, ac- 
tions, or things to be learned by the student, 
which are commonly designated, collectivelj', 
as subjects, subject-matter, objects, or object- 
matter. The intellectual activities of the teacher 
proceed under certain fixed laws of mind. His 
intellectual faculties conform to spheres of ac- 
tivity into which they are necessitated or deter- 
mined by their very nature. He cannot remem- 
ber with his faculty of imagination, nor reason 
with memory. He must perceive with his senses, 
reason with his reflective powers, and retain by 
his memory. As with the teacher so with the 
learner, whose mental faculties and capabilities 
may differ from those of the teacher in original 
quantum of functional endowment, and in de- 
grees of power, but not in kind or function. 

84. This being true, the case resolves itself 
into this : (1) If the teacher knew subject-mat- 
ter thoroughly he could arrange its parts into 
any order of dependence, or steps, or points, or 
classifications, that circumstances or exigencies 
might necessitate, or expediency demand. This 
would enable him to arrange and present his 
system of subject-matter, (2) If, in addition 



METHODS OF TEACHING. 83 

to this, he knew mind thoroughly, in its facul- 
ties, powers, capabilities, laws of growth — in 
short, in its nature and character, he would know 
exactly how to adjust the subject-matter to be 
learned to the mind that is to learn it. 
Varying circumstances of state or condition would 
not prevent this certainty of adjustment — it would 
be like the scientist adjusting the object that 
he is examining to the focus of his microscope 
so that his eye can see it in defined outline. 
(3) If, succeeding these two suppositions, the 
teacher now turns his attention for the time ex- 
clusively to consider the ways in which his sys- 
tem of subject-matter shall be set before, or in 
the presence of, those faculties which are the 
native ones to acquire learning from this sys- 
tem, — if he does this, he will be carrying on in- 
vestigations in a province which is original and 
pecidiar to the Profession of Teaching, 

85. A recapitulation of these points presents : 
(1) The first field opened for the teacher-candi- 
date is that of subject-matter to be taught by 
him, and that is to be learned by the student. 
This is the region of System, — of scholarship in 
the ordinary branches of learning as they are 
found in our schools, or as he may analyze and 
classify for presenting to his pupils. (2) The 
second field for the teacher-in-expectancy is also 
that of subject-matter, and is included within the 
range of our schools. It is special, however, to 
the Profession of Teaching, and is known by 
the name of Psychology, Mental Philosophy, or 
Intellectual Philosophy. (3) The third field is 



84 ON THE THEOKY OF 

that of the science and art of adapting object- 
matter to the capabilities of the mind to be 
taught, that of adjusting objects to the focus 
of the intellectual vision of the pupil. 

86. This is properly the Province of Meth- 
ods of Teaching. This province is that of 
Principles — it is that of those Principles which 
exist in the constitution of things, and according 
to which certain subject-matter must be ac- 
quired by the mind in a certain fixed way, pro- 
vided it ever becomes an actual knowledge 
within that mind. Some subject-matter is 
learned by one faculty, some by another. In- 
termediate between every kind of subject-matter 
and knowledge of it, there is the faculty which 
is native to the acquiring of that knowledge. 
If the proper faculty be not approached, true 
knowledge cannot be the product — from this 
conclusion there is no escape. 

87. " A principle is that which being derived 
from nothing, can hold to nothing. 

What is conmion to all first principles is that 
they are the primary source from which any 
thing is, becomes, or is known." (Fleming, 
Vocab. of Phil. ) 

88. "A Principle is a central or representa- 
tive truth in philosophy, science, art, religion, 
or morals, which is fundaniental and general, 
and out of which other matters of a speculative 
or practical character flow, and become its prac- 
tical illustration. ' He who fixes upon false 
principles treads upon infirm ground, and so 
sinks ; and he who fails in his deductions from 



METHODS OF TEACHING. 85 

right principles stumbles upon firm ground, 
and so falls. — South." (Smith, Syn. Discr., 
Doctrine.) 

' ' Principle carries knowledge with it, and is 
applicable to action as a guide or basis of pro- 
ceeding. A principle is a fundamental truth, 
or comprehensive law, from which others are 
derived, or on which they are founded. It may- 
be observed, generally, that principles are last in 
the order of investigations, and first in the order 
of practice. They are arrived at by analysis, 
and when found become bases or starting-points 
for action or scientific inquiry. " (/6idf., Prov- 
erb.) 

89. 3Iet7iods of Teaching are principles 
of adaiyting subject-matter to the capaci- 
ties and j)Oivers of the pupil. When the 
teacher says that this subject-matter should be 
presented for cognizance by this or that faculty 
of the mind, and in such and such quantities, 
according to the strength of those faculties, he is 
acting within the provi::ce of Methods of Teach- 
ing. But when the teacher says that this point 
or step of this subject-matter should succeed that 
or that step or point, he is acting within the 
scope of a System of subject-matter. 

90. These two distinct operations are often 
confounded, or used indiscriniinately, causing 
great confusion in the proper use of terms. In 
the following the word System is properly used : 
" The Gospel of St. John, adapted to the Ham- 
iltonian System, by an Analytical and Interline- 
ary Translation from the Italian, with full In- 



86 O^ THE THEORY OF 

structions for its use, even by tliose who are 
wholly ignorant of the language. For the Use 
of Schools. By James Hamilton, Author of the 
Ilamiltonian System, London, 1825." (Sydney 
Smith, Easai/s, p. 74, late ed.) In the expres- 
sion, " Grube's Method of Teaching Nmnber," 
the word Method is improperly used. It should 
be "Grube's System," because the author ar- 
ranges the subject-matter in such a way that the 
processes of addition, subtraction, multiplica- 
tion, and division, must be taught in such and such 
a sequence of order, and in such and such an 
order of steps. The teacher in this case is not 
investigating what faculties are to be incited to 
learn these steps, nor in what quantities the sub- 
ject-matter shall be set to those faculties, as 
Methods require. The same remarks apply to 
the so-called " A, B, C Method" of teaching 
children to read, the ' ' Word Method, ' ' and all 
similar expressions, where Method is used im- 
properly for System. 

91. The questions relating to what branches 
shall be taught or studied, do not belong, in 
strict analysis, to the Province of Methods of 
Teaching. They are questions of Ethics and 
of Psychology, — of the relations of the individual 
to the Family, the Society, and the State, of 
which he is a member and a part, according to 
the estimate of these relations by each people 
or nation for itself. They also are within the 
field of the development of man as man, in his 
subjective condition — that is, in his psychological 
estate. They belong to the wider field of Peda- 



METHODS OF TEACHIKG. 87 

gogics, or Education, or to what Mr. J. «. Mill 
calls " Ethology, the science of which education 
is the art." '' (Chamb. EncycL, article Educa- 
tion.) 

92. *' Ethics may be defined as the Science 
of Practice or Conduct : the latter term is pref- 
erable, as Practical Science is more conveni- 
ently used to include along with Ethics the cog- 
nate studies of Jurisprudence and Politics. 

' ' All three alike are distinguished from specu- 
lative sciences by the characteristic that they 
attempt to determine not the actual but the 
ideal : what ought to exist, not what does ex- 
ist. An objection is sometimes taken to the ap- 
plication of the term ' Science ' to such studies 
as these. It is said that a Science must neces- 
sarily have some department of actual existence 
for its subject-matter : and there is no doubt that 
the term ' Moral Sciences ' is frequently — per- 
haps more frequently — used to denote studies that 
deal with the actually existent : viz. Psychology, 
or a portion of it ; Avhat Mr. Mill calls Ethology, 
or the inquiry into the laws of the formation of 
character ; and Sociology, or (as it has also been 
termed) the Physiology of Society." (Sidg- 
wick. The Methods of Ethics, p. 1, ed. 1874, 
London.) 

93. Voluntary and conscious instruction and 
teaching are the handmaids of education, and 
are ways of approaching mind, setting before 
that mind those branches of study which Ethics 
and Psychology determine are best. 

94. Those principles of Ethics and Psychology 



88 OK THE THEOEY OF 

according to wliicli peoples, families, or individ- 
uals, determine what branches of study shall be 
pursued in schools and elsewhere, are properly- 
denominated Methods of Pedagogics. The 
term Education being used by English and Amer- 
ican authors as nearly or quite the equivalent of 
the German Pedagogics, Methods of Eduta- 
tion will be used instead of ]\Ietliods of Peda- 
gogics. Methods of Education regard the future 
man as a member of a given society ; they 
consider what the child is to become ; they 
are subjects of choice by nations, communities, 
families, or individuals, because they determine 
the uses to be made of the learning and disci- 
pline which nations or families require of the 
young. In Germany, Methods of Education are 
determined by the condition of the body-politic, 
and are well established. In France, the Meth- 
ods of Education differ from those of Germany, 
in so far as the purposes of the government differ 
from those in Germany. In England, Methods 
of Education still vary, as also they do in the 
United States. Whatever purposes Methods of 
Education propose for the young, they always 
point distinctly to the end that these young 
persons, when grown up, shall be good and loyal 
citizens of that Community or State. Methods 
of education in France are not calculated to pro- 
duce good citizens for German}^, but for France. 
It is the same with every nation. Families 
adopt Methods of Education which aim at giv- 
ing specific direction to the energies of the 
children in those families, referring immediately 



METHODS OF TEACHIKG. 89 

to the positions wliicli these chlidren shall come 
to occupy, as professional, diplomatic, or gov- 
ernmental. These Methods inquire what is to 
be studied by the learner, in order that he may 
attain a certain end desired. Methods of Teach- 
ing are concerned in Methods of Education only 
so far as to ask in what way shall the branches 
determined by the family or the nation be pre- 
sented to the mind. Methods of Teaching know 
no nationality nor family ; Methods of Education 
preserve nationality and family attainments. To 
elaborate the subject of Methods of Education 
would require an extended treatise, and must be 
set aside until a more convenient time shall pre- 
sent itself for the work. 

95. In the following quotation the province 
of Methods of Teaching is not discriminated from 
that of Methods of Education, although the no- 
tion of Method in general is very clearly out- 
lined : 

" The Methodick :— (1) The Educator must 
guide the pupil to knowledge of the outer 
world by aiding him to acquire it for himself in 
accordance with the natural operation, succes- 
sive movements or procedure of Intelligence ; — 
that is to say, according to the way or method 
whereby Intelligence proceeds and must proceed. 
These processes, as we have seen, are, in the first 
instance, Analytic, but have Synthesis and In- 
duction for their end. When ascertained, they 
yield the doctrine of Method in Education — The 
Methodick of Education. 

*' (2) The Educator must perform the same 



90 OK THE THEORY OF 

task witli reference to the liiglier feelings and 
emotions, with a view to constitute them habit- 
ual motives. In things of sense or of thought 
the learner learns by truly knowing : in things 
of action the learner learns through the action 
of others, and by his own action. The doc- 
trine of The Methodick of Education is to be 
called Methodology, and embraces the applica- 
tion of Method to every subject of intellectual 
study and to every stage of ethical training 
alike (page 16). . . . 

" The way of carrying out the Educative 
process to a successful issue, both intellectual 
and ethical, is, as we have seen, The Method- 
ick of Education (p. 18.) . . . How must 
I convey instruction so as to insure assimilation 
by the pupil ? . . . The answer to this ques- 
tion contains the Doctrine of Method, and rests 
on the process of the Will in its movements 
towards knowledge. Dependent on this are — 
Particular Methods." (Laurie, Synopsis of 
Led., p. 20, 1877.) 

96. Methods of Education have regard for the 
growth of mind as an end or habit unto itself, 
an object to be attained for itself, and also for 
knowledge or matter, as an end, (1) "What 
subjects of instruction must I teach in order to 
give to the future man the materials of right 
judgment ? (The Real.) This leads us into a 
discussion of subjects of Instruction generally 
and their relative values. (2) How must I in- 
struct so as most effectually to exercise the in- 
telligence of the pupil in making those distinc- 



METHODS OF TEACHING. 91 

tions on which the lightness of judgment de- 
pends ? (The Senses. The Formal as Will-power 
in reference to Intelligence.) The answer to the 
first of these questions contains the Doctrine of 
the Real with reference to the outer world — the 
substance of Knowledge. The answer to the 
second questions contains the Doctrine of Formal 
discipline in its intellectual relations." (Laurie, 
Syno'psis of Led., p. 20, 1877.) 

97. " It is a physiological law, first pointed 
out by Jil. Isidore St. Hilaire, and to which 
attention has been drawn by Mr. Lewes in his 
essay on Dwarfs and Giants, that there is an 
antagonism between growth and development. 
By growth, as used in this antithetical sense, is 
to be understood increase of size ; by develop- 
ment, increase of structure. And the law is, 
that great activity in either of these processes 
involves retardation or arrest of the other. A 
familiar illustration is furnished by the cases of 
the caterpillar and the chrysalis. In the cater- 
pillar there is extremely rapid augmentation of 
bulk ; but the structure is scarcely at all more 
complex when the caterpillar is full-grown than 
when it is small. In the chrysalis the bulk does 
not increase ; on the contrary, weight is lost 
during this stage of the creature's life ; but the 
elaboration of a more complex structure goes on 
with great activity. The antagonism, here so 
clear, is less traceable in higher creatures, be- 
cause the two processes are carried on together. 
But we see it pretty well illustrated among our- 
selves by contrasting the sexes. A girl develops 



93 ON THE THEOKY OF 

in body and mind rapidly, and ceases to grow 
comparatively early. A boy's bodily and men- 
tal development is slower, and his growth 
greater. At the age when the one is ma- 
ture, finished, and having all faculties in full 
play, the other, whose vital energies have been 
more directed towards increase of size, is rela- 
tively incomplete in structure ; and shows it in a 
comparative awkwardness, bodily and mental. 
Now this law is true not only of the organism as 
a whole, but of each separate part. The abnor- 
mally rapid advance of any part in respect of 
structure involves premature arrest of its growth ; 
and this happens with the organ of the mind as 
certainly as with any other organ. The brain, 
which during early years is relatively large in 
mass but imperfect in structure will, if required 
to perform its functions with undue activity, 
undergo a structural advance greater than is ap- 
propriate to the age ; but the ultimate effect 
will be a falling short of the size and power that 
would else have been attained. And this is a 
part cause — probably the chief cause — why preco- 
cious children, and youths who up to a certain 
time were carrying all before them, so often 
stop short and disappoint the high hopes of their 
parents." (Herbert Spencer, Education, pp. 
271, 272, ed. 1870.) 

" To grow is the process of which to in- 
crease is the result or manifestation. Tradp. has 
been growing for years past, and is now consid- 
erably increased. To increase, however, does 
not necessarily imply to grow ; rapid expansion 



METHODS OF TEACHIKG. 93 

or dilatation of parts will produce increase in 
bulk ; but the process of growth implies either 
an accretion of parts by external apposition, or 
an assimilative power from within, as in the vi- 
tal force. The snowball grows by accretion, 
and so increases as it rolls. The tree grows by 
its own vitality, and increases also in size." 
(Smith, Syn. Discr.) 

98. Methods of Teaching consider the growth 
of the faculties of the mind, and the quantity of 
knowledge, not as ends, but as necessary 1c tioivl- 
edge from which to project anew procedures in 
teaching while the mind of the learner is grow- 
ing. This is essential in order that the teacher 
may set to this learner, at any stage of his 
growth, the maximum quantity of subject-mat- 
ter which the present attainments and powers 
of the learner can master ; to set less than 
this amount to a pupil is puerile, and to set 
more is to prevent his powers from compre- 
hending it. Yet the faculties of mind grow into 
powers far more rapidly by attempting to com- 
prehend the unknown, the mysterious, by trying 
to enlarge the maximum degrees of efforts, than 
by resting contentedly with efforts near the 
minimum of degrees. " Mental dyspepsia" 
comes from starvation, as well as from plethora 
of subject-matter. " A well-regulated course of 
study will no more weaken the mind than hard 
exercise will weaken the body ; nor will a strong 
understanding be weighed down by its knowl- 
edge, any more than an oak is by its leaves, or 
than Samson was by his locks. He whose sinews 



94 ON THE THEOKT OF 

are drained by his liair, must already be a weak- 
ling." (Grindon, Life, p. 197.) " If the child 
of eight years old finds his improved language 
understood by a child of three, why should you 
contract yours to his vocabulary ? Always em- 
ploy a language some years in advance of the 
child (men of genius in their books speak to us 
from the vantage-ground of centuries) : speak to 
the one-year-old child as though he were two, 
and to him as though he were six ; for the 
difference of progress diminishes in the inverse 
proportion of years. Let the teacher, especially 
he who is too much in the habit of attributing all 
learning to teaching, consider that the child al- 
ready carries half his world, that of mind, — the 
objects, for instance, of moral and metaphysical 
contemplation, — ready formed within him ; and 
hence that language, being provided only with 
physical images, cannot give, but merely illum- 
ine, his mental conceptions." (Richter, Le- 
vana, pp. 347-8.) 

99. In this immediate connection it will be 
profitable to give a brief attention to the pop • 
nlar expression, " Teachers should teach pupils 
how to learn, how to use their faculties in order 
that they shall be able to continue their mental 
activities by themselves, in subsequent years. " 
It is a plain fact in psychological phenomena, 
that nearly all the faculties of mind grow, " in- 
crease in size," by exercise. This is emphatically 
true of the faculties of Thought and Attention, 
which are energies of the Will. Education is a 
habit. Hence no one can be said to know how 



METHODS OF TEACHIiq-G. 95 

to command liis faculties, wlio lias not tlie habit 
of it, called education. This state is attained 
by those, and those only, who actually exert 
their faculties to the maximum degrees, so that 
this state becomes habitual. Methods of Teach- 
ing regard these degrees as their bases in Mind. 
Mere Theory will never produce these habits. All 
teaching of pupils " how to study," which does 
not demand of them their maximum efforts in 
practice, is a delusion, and a fatal deception to 
the learners. The arm of the smith does not 
grow strong by his standing at the forge and 
looking at the sledge-hammer, but by wielding 
it. Intellectual growth comes not by thinking 
how to study, but by mental application in 
studying up to the measure of the highest de- 
grees. 

100. So far as Methods of Teaching are con- 
cerned, the matter taught may be in itself, 
either error or truth. Methods take whatever 
subjects, in whatever form of text-books or ob- 
jects, that are set to them, and convey them into 
the presence of the corresponding faculties that 
are to learn these subjects — this conveying, if ac- 
cording to a philosophical principle, is teaching ; 
for no power external to the mind of the learner 
can learn for that mind, nor compel it to learn. 
The learning is a matter within the exclusive 
province of the mind that is to learn, or to be 
taught. 

101. Methods of Teaching are not concerned 
with what is popularly called " waking up 
mind," for if Methods assume any thing pre- 



96 ON THE THEOEY OF 

eminently, it is tliat subject-matter, when set 
before mind according to the principles of adap- 
tation, will incite the mind to activity, intui- 
tively and spontaneously. " To wate up mind, " 
implies, in practice, the false notion that the chil- 
dren are to be excited or astonished at the man- 
ner of the teacher, and at the irrelevancy of the 
points he presents, rather than at the value of 
the subject-matter set before them to be learn- 
ed. This is mere charlatanism. Emotional ex- 
citement, with dissipation of thought, can never 
take the place of calm, deliberate, intense atten- 
tion and continued thinking, when sound learn- 
ing is sought. Nothing is more pernicious to 
good habits of thought than the introduction 
into class-rooms of what is called '' variety," as 
the term is practically exemplified. The only 
" variety" permissible, is that which follows upon 
progress, pointedly, into additional subject-mat- 
ter of the lesson, not into this or that subject 
which has no direct and close relationship to the 
recitation, and which permits attention and power 
to be dissipated, not concentrated. The mind 
of childhood is always awake — it may need to 
be centred on this subject. 

102. " Bonnet calls attention the mother of 
genius, but she is in fact her daughter ; for 
whence does she derive her origin, save from 
the marriage contracted in heaven between the 
object and the desire for it ? Hence attention 
can really be as little preached or flogged into 
a person as ability. ... A very important 
distinction must be drawn between the power of 



METHODS OF TEACHING. 97 

attention diffused among the generality of men, 
and that appertaining solely to men of genius. 
The latter can only be recognized, protected, and 
cherished, but not created. . . . On the 
other hand, common every-day attention needs 
not so much to be aroused, as to be distributed 
and condensed ; even careless, inattentive chil- 
dren possess the faculty, but it is dissipated upon 
all passing objects. ... In what manner 
can you arouse the innate desire of mental prog- 
ress ? The impulses of the senses excite and 
then stupefy, but help not to produce it. To 
overwhelm the mind with lessons, that is, w^ith 
mere summaries of accounts, resembles the Si- 
berian custom of giving the sacrament of the 
Lord's Supper to infants. . . . Philosophy 
begins with what is highest and most difficult ; 
mathematics, with Avhat is nearest and easiest. 
What, then remains ? The metaphys- 
ics of the eye ; the knowledge forming the 
boundary between experience and abstraction.'* 
(Richter, Levana, pp. 353-9.) 

103. " To Excite (Latin, excitare) is to call 
out into greater activity what before existed 
in a calm or calmer state, or to rouse to an 
active state faculties or powers which before 
were dormant. The term is also used of purely 
physical action. We excite heat by friction. 
Awaken (A. S., awaccian, awecian) is to 
rouse from a state of sleep, or, analogously, to 
rouse any thing that has lain quiet, and, as it 
were, dormant, as to awaken suspicion, and is 
applicable only to intelligent subjects. Rouse 



98 OK THE THEORY OF 

(A. S. , rasian) is to awaken in a sudden or start- 
ling manner, so as to bring into an energetic 
state by a strong impulse. To incite (Latin, 
incitare) is to excite to a specific act or end 
which the inciter has in view. To stimulate is 
to quicken into activity (stimulus, a spur) 
and to a certain end. Men are incited when 
their passions are roused-; they are stimulated 
when they are induced to make greater exer- 
tions, as by a hope of reward or any other exter- 
nal impulse. They are awakened out of indiffer- 
ence, roused out of lethargy and torpor, incitei 
by the designing influences of others, stimulated 
by new motives of action. Men are incited to 
what otherwise they would not have given their 
efforts. They are commonly stimulated to 
something which they are pursuing, or intend 
ing to pursue, but with want of energy 
(Smith, Syn. Discr.) 

104. As to the Form in which knowledge 
is left in the mind, when all the circumstances 
attending the presentation have been rigidly 
based upon the nature of the case. Methods of 
Teaching have no responsibility — that ends when 
the presentation is completed. The mind, as a 
cause unto itself, and its prior state of knowl- 
edge, are responsible for the form or impression, 
in which the matter, under these conditions, ex- 
ists within itself. If this form lacks certitude, 
or " material truth in the absolute sense," it 
can only be corrected by presenting to the learn- 
ing mind other subject-matter. But what this 
subject-matter shall be is no concern of Methods 



) ) 



METHODS OF TEACHING. 99 

of Teaching, as has been shown in a previous 
section of this investigation. If the subject-mat- 
ter be not properly separated into parts, and 
those parts sharply freed from adventitious mat- 
ter, so that it may be brought boldly and une- 
quivocally into the conscious presence of the cor- 
responding faculties — if there be a want here, 
it is the fault of the System of the teacher. 
Methods of Teaching demand only that the prin- 
ciples of adaptation he not violated. The 
Methods assume the subjects placed in the hands 
of the teacher. The teacher has two important 
things to do : (1) To consider if his System of 
subject-matter is so constructed that it is capa- 
ble of being presented to this individual learner ; 
(2) To reflect upon the principles which under- 
lie the actual procedure of teaching. He must 
attend to System and then to Method. 

105. In connection with Methods of Teaching 
one often 'hears the expressions, " Develop the 
idea in the mind of the learner," " Lead the 
mind gradually up to the idea. ' ' To simple per- 
ception there can be no development work, for 
perception is intuitive, and is ultimate in its au- 
thority, upon the presence in consciousness of 
the object. Development exists within the Prov- 
ince of Thought. 

Notions, or conceptions, or ideas, are aggre- 
gations of simpler elements, which constitute the 
group or Unit of notions. When the faculties of 
the mind are too feeble to comprehend the unit 
group, the elements of the unit are separated 
and set before the mind of the learner in sue- 



100 OK THE THEORY OF • 

cession until all are seen as one. The process 
(Mode), called " development," is tliat by which 
the teacher analyzes and presents the notion that 
is to be taught, and the synthetical process by 
which the learner apprehends, and combines or 
reconstructs, the elements into a notion that is 
similar to that possessed by the teacher. 

106. The process by which a student is in- 
ducted into a prehension and a comprehension 
of an aggregation of ideas, which bear an inti- 
mate and necessary relation to each other, is 
called Thoroughness. A student who is thor- 
oughly taught surveys from the centre, a group 
of ideas which constitute a structure created by 
Thought. 

107. " To Develop is to open out what was 
contained in another thing, or the thing itself 
(Fr. developper). In develop these two ideas 
are inherent, the gradual opening of the whole 
containing, and the gradual exhibition of the 
particular contained. So we might say, ' Time 
developed his character,' or ' circumrtances de- 
veloped the cruelty which was latent in his char- 
acter. ' Unlike Unfold, develop is not used of 
purely physical processes. We speak of the de- 
velopment of plans, plots, ideas, the mind ; and 
also of the development of the body in growth ; 
but these are scientific terms involving other 
ideas, as of the vital functions in growth. We 
should never speak of the development of a flag 
or a tablecloth. In other words, it is not used 
of manual or mechanical unfolding. On the 
other hand, in the sense of the mechanical pro- 



METHODS OF TEACHING. 101 

cess of gradually opening, unfold is used as well 
as in the other ; but in this latter develop ex- 
presses far more than unfold, and relates to the 
laws of expansion by which a thing unfolds in 
definite sequence of expansion, and in conform- 
ity with principles which conserve the type de- 
veloped. Hence we speak of a true and a vic- 
ious development. To Unravel (old German, 
reiFen, to pluck) is purely a mechanical effort of 
separating what is complicated, whether naturally 
or accidentally, and expresses simple disentangle- 
ment, not growth or expansion. As the former 
indicate ordinary processes of nature or art, so 
the latter indicates extraordinary and counterac- 
tive processes, and commonly implies the abnor- 
mal state of that which needs to be unravelled. 

" * Then take him to develop if you can, 

And hew the block off and get out the man. ' 

Pope. 

** * Several pieces of cloth, the largest we had 
seen being fifty yards long, which they un- 
folded and displayed so as to make the greatest 
show possible.' — Cook^s Voyages. 

' ' ' What riddle's this ? tlnfold yourself, dear 
Robin. ''—Ben Jonson. 

' ' ' That great chain of causes which, linking 
one to another, even to the throne of God Him- 
self, can never be unravelled by any industry of 
ours.' — Biirke.^^ (Smith, Syn. Discr., ed. 
1878, Develop.) 

108. Methods of Teaching must have refer- 
ence-to the ways according to which the learner's 



102 OK THE THEORY OF 

faculties proceed tvlien he is apjylying Jiim- 
self to study. Unless this be understood, the 
faculties of the pupil will be embarrassed in their 
normal activities. This will cause discourage- 
ment to both teacher and pupil. 

109. " There exist nevertheless certain gen- 
eral modes of treating any subject which can be 
clearly distinguished by the student. Logic 
cannot teach him exactly how and when to use 
each kind of method, but it can teach him the 
natures and powers of the methods, so that he 
will be more likely to use them rightly. We must 
distinguish : 

"1. The method of discovery, 

*' 2. The method of instruction. 

*' The method of discovery is employed in 
the acquisition of knowledge, and really consists 
in those processes of inference and induction, by 
which general truths are ascertained from the 
collection and examination of particular facts. 
The second method only applies when knowl- 
edge has already been acquired and expressed in 
the form of general laws, rules, principles or 
truths, so that we have only to make ourselves 
acquainted with these and observe the due mode 
of applying them to particular cases, in order to 
possess a complete acquaintance with the subject. 

" A student, for example, in learning Latin, 
Greek, French, German, or any well-known lan- 
guage, receives a complete Grammar and Syntax 
setting forth the whole of the principles, rules 
and nature of the lano-uao'e. He receives these 
instructions, and takes them to be true on the 



METHODS OF TEACHIiq-G. 103 

authority of the teacher, or the writer of the 
book ; and after rendering them familiar to his 
mind he has nothing to do but to combine and 
apply the rules in reading or composing the lan- 
guage. He follows, in short, the method of In- 
struction. But this is an entirely different and 
opposite process to that which the scholar must 
pursue who has received some writings in an un- 
known language, and is endeavoring to make out 
the alphabet, words, grammar, and syntax of the 
language. He possesses not the laws of gram- 
mar, but words and sentences obeying those 
laws ; and he has to detect the laws if possible 
by observing their effects on the written lan- 
guage. He pursues, in short, the method of dis- 
covery consisting in a tedious comparison of let- 
ters, words, and phrases, such as shall disclose 
the more frequent combinations and forms in 
which they occur. The process would be a 
strictly inductive one, such as I shall partially 
exemplify in the Lessons on Induction ; but it is 
far more difficult than the method of Instruction, 
and depends to a great extent on the happy use 
of conjecture and hypothesis, which demands a 
certain skill and inventive ability. 

" Exactly the same may be said of the inves- 
tigation of natural things and events. The prin- 
ciples of mechanics, of the lever, inclined plane, 
and other Mechanical Powers, or the Laws of 
Motion, seem comparatively simple and obvious 
as explained to us in books of instruction. But 
the early philosophers did not possess such 
books ; they had only the Book of Nature, in 



104 Oiq" THE THEORY OF 

wliich is set forth not the laws, but the results of 
the laws, and it was only after the most patient 
and skilful investigation, and after hundreds of 
mistakes, that those laws were ascertained. It 
is very easy now to understand the Copernican 
system of Astronomy, which represents the plan- 
ets as revolving round the sun in orbits of vari- 
ous magnitude. Once knowing the theory we 
can readily see why the planets have such var- 
ious movements and positions, and why they 
sometimes stand still ; it is easy to see, too, 
why in addition to their own proper motions 
they all go round the earth apparently every day 
in consequence of the earth's diurnal rotation. 
But all these changes were exceedingly puz- 
zling to the ancients, who regarded the earth as 
standing still. 

" The method of discovery thus begins with 
facts apparent to the senses, and has the difficult 
task of detecting those universal laws or general 
principles which can only be comprehended by 
intellect. It has been aptly said that the method 
of discovery thus proceeds from things better 
known to us, or our senses (nobis notiora), to 
those which are more simple or better known in 
nature (notiora naturae). The method of In- 
struction proceeds in the opposite direction, be- 
ginning with the things notiora naturae, and 
proceeding to show or explain the things nobis 
notiora. The difference is almost like that be- 
tween hiding and seeking. He who has hidden 
a thing knows where to find it ; but this is not 
the position of a discoverer, who has no clue ex- 



METHODS OF TEACHING. 105 

cept such as he may meet in his own diUgent 
and sagacious search. 

' ' Closely corresponding to the distinction be- 
tween the methods of Discovery and Instruction 
is that between the methods of Analysis and 
Synthesis. It is very important indeed that the 
reader should clearly apprehend the meanings of 
these terras in their several applications. Analy- 
sis is the process of separating a whole into its 
parts, and synthesis the combination of parts 
into a whole. The analytical chemist, who 
receives a piece of mineral for examination, 
may be able to separate completely the several 
chemical elements of which it is composed and 
ascertain their nature and comparative quantities ; 
this is chemical analysis. In other cases the 
chemist mixes together carefully weighed quan- 
tities of certain simple substances and combines 
them into a new compound substance ; this is 
chemical synthesis. Logical analysis and syn- 
thesis must not be confused with the physical 
actions, but they are nevertheless actions of 
mind of an analogous character. 

" In logical synthesis we begin with the 
simplest possible notions ' or ideas, and combine 
them together. We have' the best possible ex- 
ample in the elements of Geometry. In Euclid 
we begin with certain simple notions of points, 
straight lines, angles, right angles, circles, &c. 
Putting together three straight lines we make a 
triangle ; joining to this the notion of a right 
angle, we form the notion of a right-angled tri- 
angle. Joining four other equal lines at right 



106 Oi^ THE THEORY OF 

angles to eacli other we gain the idea of a 
square, and if we then conceive such a square 
to be formed upon each of the sides of a right- 
angled triangle, and reason from the necessary- 
qualities of these figures, we discover that the 
two squares upon the sides containing the right 
angle must together be exactly equal to the 
square upon the third side, as shewn in the 
47th Proposition of Euclid's first book. This is 
a perfect instance of combining simple ideas into 
more complex ones. 

" We have often, however, in Geometry to 
pursue the opposite course of Analysis. A 
complicated geometrical figure may be given to 
us, and we may have, in order to prove the prop- 
erties which it possesses, to resolve it into its 
separate parts, and to consider the properties of 
those parts each distinct from the others. 

' ' A similar distinction between the analytical 
and synthetic methods can be traced throughout 
the natural sciences. By keeping exact registers 
of the appearance and changes of the weather 
we may readily acquire an immense collection of 
facts, each such recorded fact implying a multi- 
tude of different circumstances occurring to- 
gether. Thus in any storm or shower of rain 
we have to consider the direction and force of 
the wind ; the temperature and moistness of the 
air ; the height and forms of the clouds ; the 
quantity of rain which falls, or the lightning 
and thunder which occur with it. If we pro- 
ceed by analysis only to explain the changes of 
the weather we should have to try resolving 



METHODS OF TEACHING. 107 

eacli storm or change of weather into its separate 
circumstances, and comparing each with every 
other to discover what circumstances usually go 
together. We might thus ascertain no doubt 
with considerable certainty what kinds of clouds, 
and what changes of the wind, temperature, 
moisture, &c., usually precede any kind of 
storm, and we might even in time give some im- 
perfect explanation of what takes place in the 
atmosphere. 

' ' But we might also apply with advantage 
the synthetical method. By previous chemical 
investigations we know that the atmosphere 
consists mainly of the two fixed gases, oxygen 
and nitrogen, with the vapour of water, the latter 
being very variable in quantity. "We can try 
experimentally what takes place when portions 
of such air of various degrees of moistness are 
compressed or allowed to expand, or are mixed 
together, as often happens in the atmosphere. 
It is thus discovered that whenever moist air is 
allowed to expand cloud is produced, and it may 
be drops of rain. Dr. Ilutton, too, found that 
whenever cold moist air is mixed with warm 
moist air cloud is again produced. We can 
safely argue from such small experiments to 
what takes place in the atmosphere. Putting 
together synthetically, from the sciences of 
chemistry, mechanics, and electricity, all that 
we know of air, wind, cloud and lightning, we 
are able to explain what takes place in a thunder- 
storm far more completely than we could do by 
merely observing directly what happens m the 



108 OK THE THEORY OF 

storm. We are here however anticipating the 
methods of inductive investigation, which we 
must consider in the following lessons. It will 
appear that Induction is equivalent to analysis, 
and that the deductive kinds of reasoning which 
we have treated in prior lessons are of a synthetic 
character. 

' ' It has been said that the synthetic method 
usually corresponds to the method of instruction 
and the analytic method to that of discovery. 
But it may be possible to discover new truths by 
synthesis and to teach old ones by analysis. Sir 
John Herschel in his well-known Outlines of 
Astro7iomy partially adopts the analytic method ; 
he supposes a spectator in the first place to survey 
the appearances of the heavenly bodies and the 
surface of the earth, and to seek an explanation ; 
he then leads him through a course of arguments 
to show that these appearances really indicate 
the rotundity of the earth, its revolution about 
its own axis and round the sun, and its subor- 
dinate position as one of the smaller planets of 
the solar system. Mr. Norman Lockyer's Ele- 
mentary Lessons in Astronomy is a clear example 
of the synthetic method of instruction ; for he 
commences by describing the sun, the centre of 
the system, and successively adds the planets 
and other members of the system, until at last 
we have the complete picture ; and the reader 
who has temporarily received everything on the 
writer's authority, sees that the description cor- 
responds with the truth. Each method, it must 



METHODS OF TEACHING. 109 

be allowed, has its own advantages. (Jevons, 
Lesso7is in Logic, ed. 1878, pp. 202-208.) 

110. Methods of Teaching must respect that 
inherited and national "cast of mind" which 
exhibits itself so prominently that it forms an 
important element in teaching. Those national 
bents of mind, traits of disposition, and survival 
of tendencies, constitute a " prior knowledge," 
or setting, which gives form to the knowledge 
presented by the teacher. The Italian mind in- 
herits peculiar adaptations for music. The Ger- 
man mind, as revealed in the language, is dis- 
posed to aggregate and accumulate conceptions. 
The native tendency with the French mind, in 
language, is towards separation and analysis. 
The English mind, in language, evidently has 
its form in directness, neither cumulative nor 
over analytical. With some nations, gesticulation 
forms a prominent inheritance of the people. 
The United States, being peopled from all na- 
tions, present a multitude of national peculiari- 
ties to the teacher, who, herein, has a more deli- 
cate work before him than teachers who labor 
with a single nationality. This element, although 
subtle, is powerful in any place where the schools 
are composed of children of many nationahties. 
"While the psychological faculties are the same 
in kind and function among all peoples, yet the 
native quality of these faculties, or the bent 
for giving form to knowledge, varies with the 
peoples. These native qualities or bents are not 
the differences in degrees of the same capacities 
of people of the same nationality. They are 



110 OK THE THEORY OP 

powers or forces wliicli necessarily modify the 
form of the same matter which is set before all 
alike. This is done miconsciously to the chil- 
dren who are taught. 

111. Methods of Teaching are difficult to 
suit, " as an object to a quality," in their daily 
application, by reason of the intricacy and eva- 
nescence of psychological phenomena. But the 
province is established. The very delicacy and 
mutability of the modifications of Mind lend a 
zest to Methods, and consequently to teaching, 
that must emphatically and forever banish all 
tendencies to mere routine and formalism, when 
teachers fully grasp the Spirit of Methods. Gen- 
nine Methods of Teaching, from their nature, 
must be universally successful for accomplishing 
their objects. A principle can never become 
spiritless — the application of it may, if it be an 
unintelligent one, but the principle must be as 
constant and as enduring as the subjects to which 
it relates, or out of which it springs. 

112. Methods of Teaching are not, in the 
present state of psychological science, absolutely 
invariable. The one element in the foundations, 
that of subject-matter, is firm, as science is firm. 
The other element in the foundations, that of 
psychology, is less firm, perhaps, because the Sci- 
ence of Mind is not so well established in its full- 
ness as are most other sciences which are pursued 
in schools. No science or art is more stable or 
lasting than its foundations. However, the main 
principles of the science of psychology are very 
thoroughly established, as they appear to-day 



METHODS OF TEACHIKG. Ill 

rising up out of hundreds of years of diligent 
study by tlie philosophers of the past and the 
present. " In mental philosophy the general 
statements have commonly a genuine fact, but 
mixed with this there is often an alloy. The 
error may not influence the spontaneous action 
of the primitive principle, but it may tell disas- 
trously or ludicrously in the reflex application. ' ' 
(McCosh, Int. of Mind, p. 60, ed. 1870.) 

113. What are ordinarily denominated ' ' class- 
drill" and "examinations," are no legitimate 
elements in the conception of Methods of Teach- 
ing. They are no new things — they are mere 
repetitions. The value of repetition is purely a 
psychological problem, not belonging to subject- 
matter and mind, as do the problems of Methods. 
" Repetition, else the mainspring of instruction, 
is the chief destroyer of attention ; because, in 
order to give attention to what is repeated, you 
must first have found it worthy of a still greater 
exertion of that faculty." (Richter, Levana, p. 
356.) 

114. Methods of Teaching, from their nature, 
forbid the so-called Individuality of any teacher 
to enter into them, as a constituent part of their 
essence. The foundations of the Methods being 
the principles of adaptation between subject- 
matter and mind, the eccentricities, idiosyncra- 
sies, or peculiarities of any one mind form no fac- 
tor in the Science and Art of Methods of Teach- 
ing. *' Every mind is more or less like every 
other mind ; there is always a basis of similarity, 
but there is a superstructure of feelings, im- 



112 OK THE THEORY OF 

pulses, and motives whicli is distinctive for each 
person." (Jevons, Princ. of Science, p. 733, 
ed. 1877.) 

115. Teachers have their individuaUty, which 
shows itself in greater or less degrees in their 
school-room practice, while applying philosophi- 
cal Methods of Teaching. This individuality is 
exhibited in the way that one teacher illustrates a 
point differently from another — in the way he 
speaks — in the way he looks — in the way he 
thinks, it may be — in the way in which his 
questions are conceived — in the impromptu ex- 
pedients which he devises — in what, in general, 
is called '* his way of doing things." This in- 
dividuality of the teacher is known as Manner. 
Misapprehension of the true province of scientific 
Methods of Teaching has led many to apply the 
term to any peculiar experiment or expedient 
which may be selected, which things are in fact 
but examples of Manner. The familiar expres- 
sions so often heard — ' ' my method is thus and 
so, " * ' my method is not that, but this, " " I 
illustrate by this method, using a bundle of 
sticks instead of kernels of corn' ' — are simply ex- 
amples of Manner. 

116. A teacher has his own Manner of 
Teaching — he can not have his 3Iethod^ be- 
cause Methods are general or universal principles, 
which are beyond the exclusiveness of the indi- 
vidual. Mannerisms can be affected or imitated, 
or devised, or invented ; but Methods of Teach- 
ing, existing originally in the native constitution 
of things, can not be invented — they must be 



METHODS OF TEACHIITG. 113 

discovered. Being discovered, they are no^ 
more his who discovers them, than the principle 
of gravity is the property of Newton because he 
discovered its nature and laws. 

117. This conception of Methods of Teaching 
should not be confused with that of Methods in 
general, which are ways of procedure in the in- 
vestigations of subject-matter only — they do not 
aim at mind. Such expressions as " Horner's 
Method of Approximation," and the like, cor- 
rectly use the word Method. 

118. In the subjoined quotation the terms 
Manner and Method are not sufficiently discrimi- 
nated in demarcation — each includes portions of 
the conception of Mode. 

" Perhaps this difference between method and 
manner will appear better if we use an illustration 
which is supported by the etymology of the 
word method : Suppose it is proposed to estab- 
lish a connection between two cities, for this 
purpose a road is made ; this road will be used 
by all that go from one city to the other, and by 
all kinds of individuals ; it is the same road 
for all and not liable to be changed by individual 
whims or notions. But the manner in which 
the road is used varies very much ; some will 
walk, others will run, and others still will ride. 
The road in our illustration represents the 
method in pedagogics ; it may be used by the 
most widely different individualities ; the way 
in which people make use of it is the manner. 
Manner cannot be thoroughly specified or de- 
fined. Here the utmost freedom must be allowed 



114: OK THE THEORY OF 

^o teachers and pupils to develop tlieir own in- 
dividualities. " (Soldan, art. Method and Man- 
ner, Nat. Ed. Ass. Proceedings, 1874, p. 249.) 

119. When the Manner of a teacher has 
*' method in it," — when it is more or less deter- 
mined into a System — when it has become a 
somewhat systematized exposition or application 
of the principle of adaptation, i.e., of Methods 
of Teaching, — when Manner has assumed this 
state, it is called Mode. 

120. Methods of Teaching are fundamental 
and general principles " out of which other 
matters of a speculative or practical character 
flow, and become its practical illustrations" — 
they must be discovered, if known. They can 
be investigated in their nature — they can not be 
copied, imitated, or assumed — they can only be 
stated as principles, which can be illustrated or 
exemplified in practice in certain ways called 
Modes, and sometimes Manners. Manner is the 
term which contains prominently the individual- 
ity of the teacher. Mode refers to the systematic 
application or illustration of Methods — it has lit- 
tle of the notion of individuality in it. Manner 
can be imitated, but hardly taught. Mode 
can be imitated and taught. If a teacher writes 
out a lesson in a methodical order, point by point, 
and question by question, such lesson is his Mode 
— and it may partake of his Manner. The more 
nearly teachers comprehend the nature of sub- 
ject-matter as related to knowing mind, and the 
mind itself, the more nearly will their Modes be 
identical when teaching the same subject-matter 



METHODS OF TEACHING. 115 

to classes of similar attainments — and tlie less of 
mannerisms will be exhibited by the teachers. 

121. If perfection of knowledge and of 
adaptation were possible, it is extremely prob- 
able that all perfect teaching would set the 
same subjects to the same pupils in exactly the 
same Mode, which would then reach a perfect 
illustration of Method of Teaching. 

122. The failure to discriminate the prov- 
inces of Methods of Teaching, Modes, and 
Manners, has led to considerable abuse of the 
former expression. Mode and Manner can be 
imitated by those even who do not comprehend 
the principle which is illustrated ; supposing a 
principle involved in the case, which principle is 
sometimes wholly imaginary in actual practice. 
This being the state of affairs, teachers who rest 
satisfied with copying another's Mode or Manner 
must fail, because they do not apprehend the 
animating principle, the Method of Teaching, 
which underlies the Mode imitated. Those 
teachers are dealing with the mere dress, lifeless 
forms, of Methods. Methods are life, enduring 
as mind. Modes have a portion of the life of 
Methods, and a portion from that of the teacher. 
Manner has only the life of the teacher whose 
it is. 

123. " While Mode (Lat. modus) is also ap- 
plicable to way of being, Manner (Fr. maniere) 
denotes way of action. Manner, too, is casual ; 
mode, systematic. Mode might be defined reg- 
ular manner. Hence manner of action im- 
plies voluntariness on the part of the agent ; 



116 OK THE THEORY OF 

mode of action, uniformity in the thing acting. 
Modes of existence. Manners of conduct or oper- 
ation." (Smith, Syn. Discr., Mode.) "In 
consequence of the authorship — there being a 
large number of different writers — there is great 
variety in the modes of treatment." (The 
Nation, No. VOO, p. 340, Nov. 28, 1878.) 
" We al] remember how rapidly the theory 
grew up that in the greenbacks we had stumbled, 
by a happy accident, on a new mode of acquir- 
ing wealth and avoiding financial convulsions, 
and how rapidly, too, in many minds, they began 
to wear the air of weapons of war, like a grand- 
father's sword or musket, hallowed by associa- 
tions, and unfit subjects for scientific examination 
or treatment." {Ihid., No. 704, p. 394, Dec. 
26, 1878.) " Washburn's Outlines of Criminal 
Laiv. A Manual of Criminal Law, including the 
Mode of Procedure by which it is enforced." 
{Ihid., No. 704, Dec. 26, 1878.) 

124. "System {Gr.' avGTfjjda, from avri- 
GTaraiy to place together) regards fixed sub- 
jects which have rational dependence or con- 
nection. Method (Gr. jjsra, after, and odo^y 
a way) regards fixed processes. System is logi- 
cal or scientific collocation. Method is logical 
or scientific procedure. But, inasmuch as a 
mode of procedure may be itself harmonized, 
system is frequently used in place of method. 
W"e sometimes say, ' to go systematically to 
work,' meaning methodically. Method lays 
down rules for scientific inquiry, and is the way 
which leads to system. ' All method,' says Sir 



METHODS OF TEACHING. 117 

W. Hamilton, * is a rational progress — a prog- 
ress toward an end. ' When VVatts says, ' The 
best way to learn any science is to begin with a 
regular system, or a short and plain scheme of that 
science well drawn up into a narrow compass, ' 
he is recommending a method." (Smith, Syri. 
Discr., art. S^jstem.) " System is a connected 
body of knowledge. ' ' (Jevons, El. Les, Logic, 
p. 346.) 

125. In the following quotation, the defini- 
tions are not strictly accurate, although they ex- 
press the outlines : — " In pedagogy, method is 
the way chosen, the order followed by the teacher 
to put his own thought, his intelligence, in re- 
lation with the intelligence of his pupils ; mode 
is the way of organizing the school according as 
it is desired to convey lessons directly or indi- 
rectly to the pupils ; and procedures are the 
secondary means, ordinarily mechanical, which 
are used to assure the success of the method. 
They depend generally on the mode adopted." 
(L. Mariotti, Conferences de Pedagogic, p. 146, 
ed. 1873, Paris.) 

126. In the following quotation {h), or 
*' Applied," under both the general and the 
special, contains the conception of Mode. 

"Definition of Method. 

"General: {a) Theoretical: — The laws ac- 
cording to which the ten- 
dency to acquire knowledge, 
exerts itself, arranged so as 



118 OiT THE THEORY OF 

to sliow their natural order 
and relations. 

(b) Applied: — The same laws 
translated into rules, and ar- 
ranged in the same order. 
'* Special: (a) Theoretical: — The laws ac- 
cording to which the ten- 
dency to acquire a knowl- 
edge of Physics, Logic, &c., 
■exerts itself, arranged so as 
to show iiieir natural order 
and relations. 

(b) Applied: — The same laws 
translated into rules, and ar- 
ranged in the same order." 
(The late J. W. Arm- 
strong, D.D. — A Paper on 
Method. ) 

127. " The tendency of any power or force 
to act in any particular way is called a Principle. 
The particular way in which a tendency operates 
is called a Law. The statement of a law in such 
form as will adapt it to the solution of problems 
is called a Rule." (Ibid.) 

128. (a) Method, Mode, and Manner of 
Teaching, may be illustrated and contrasted, per- 
haps not inaptly, by the following supposition : 
Suppose an engineer desires to span a stream by 
a bridge — (1) he rears his abutments on either 
side — (2) he places the main timbers or " string- 
ers" from abutment to abutment across the chasm 
— (3) he lays a roadway of planks upon the 
stringers — (4) he travels across the gulf upon 



METHODS OF TEACHING. 119 

the bridge. Tn the analogy, (1) rearing the abut- 
ments corresponds to the acquisition of a knowl- 
edge of subject-matter (say arithmetic), and of 
mind of the learner (Psychology), by the teacher 
— (2) throwing the stringers across the stream 
illustrates the process of discovering the principles 
of adjusting subject-matter to the mind of the 
learner, which is the Method of Teaching — (3) 
covering these stringers (which represent the 
principles of connection) with a flooring of what- 
ever nature, suggests the invention of a Mode of 
Teaching — (4) the general or the particular 
' ' air, " or " style, " or " bearing, ' ' of the 
teacher while teaching (crossing the bridge) indi- 
cates his Manner of Teaching. Manner also in- 
cludes a little of the notion of the flooring, as 
that a part of it is laid of wood, a part of iron, 
according to the fancy of the engineer. 

(b) Another illustration : — " Another thing — 
at Hillard on the Pacific railway — on the use of 
which Eastern people venture queer conjectures, 
is a high, narrow tressel-work bridge supporting 
a Y-shaped trough — an object familiar enough to 
residents of the Pacific Coast. This is a ' flume, ' 
and the wood used in the kilns is floated through 
it for a distance of twenty-four miles from the- 
mountains. Over 2,000,000 feet of lumber 
were necessary in its construction, and from 
its mouth it falls 2,000 feet, the stream rush- 
ing through it and sweeping the logs on its 
bosom with a rapidity and ease that makes us 
wonder why people ever haul wood in cumber- 
some waggons." (D. Appleton & Co., The Art 
Journal J New Series, No. 27, p. 71.) ' 



120 OK THE THEOEY OE 

In this illustration, the principle of conveyance 
is known in popular language as the " buoying 
up power of water," the relative specific gravity. 
This is the Method, — by floating on water. The 
contrivance, a V-shaped trough, instead of the 
surface of a river, exhibits the Mode of applying 
the principle or Method. Whatever is peculiar, 
or individual about the trough, or the prepara- 
tion of the wood, or the letting of the water into 
the flume, indicates the Manner involved in the 
case. 

(c) Another illustration : — " A railroad has 
been constructed to the mines of Summit Hill, 
about nine miles W. of the town (Mauch Chunk 
— Mawk Chunk' — in Pennsylvania). The cars, 
loaded wdtli coal, descend by their own gravity 
to the landing, and after being emptied have 
been heretofore drawn up the plane by mules. 
But now the labors of the mules are superseded. 
A ' back track ' has been constructed, which is 
regarded as a master piece of bold and success- 
ful engineering. From the chutes where the 
coal cars are unloaded at the town of Mauch 
Chunk, they return by their own weight to the 
foot of Mount Pisgah. They are then drawn 
to the top of that mountain on an inclined plane 
by means of a stationary engine. From the 
head of this plane they pass by their own gravity 
along a railway of 6 miles, to the foot of 
another inclined plane. To the top of this they 
are again raised by steam, and thence descend to 
the different mines, where they are filled with 
coal, and again descend by their own weight to 



METHODS OF TEACHIITG. 121 

the chutes." (J. Thomas, LippincotVs Pro- 
nouncing Gazetteer, ed. 1868, Mauch Chunk.) 

In this illustration, three principles of motive 
power are introduced — gravity, animal-power, 
and steam. They are the Methods of transpor- 
tation. The principle of gravity is utilized by 
carriages on wheels, instead of carriages on run- 
ners ; the principle of animal-power was utilized 
by using mules, instead of horses ; the principle 
of steam-power is utilized by means of a sta- 
tionary, instead of a movable, engine. The car- 
riages on wheels, the mules, and the stationary 
engine, are objects which are used to apply the 
Methods, and are Modes of transportation. 
Whatever is individual, or peculiar, in any of 
these — not necessary, used instead of something 
else in form, rate of motion, or way of applica- 
tion, or in construction, — exhibits Manner. 

(d) Another illustration : — A gentleman em- 
ploys a span of horses to draw his carriage. 
Horse-power is the principle involved in convey- 
ing — it is the Method of transporting the car- 
riage. A carriage on wheels is used, instead of 
a sleigh, or ' ' carriage on runners, ' ' as the way 
of showing the application of the principle of 
horse-power — this represents the Mode of con- 
veyance used by the gentleman. His particular 
kind of carriage is a landau, instead of a wag- 
onette — this notion, together with whatever of 
*"* style, " or " air, ' ' he may choose to introduce, 
exhibits his Manner of riding in his landau. 
(See, also. Mill's use of these terms in § 224.) 

129. Mr. Page uses Mode correctly in this : 



122 OK THE THEOEY OF 

" Eight Modes of Teaching — Pouring-in Pro- 
cess, or lecturing ; Drawing-out Process, or 
questioning." (Theory and Practice of Teach- 
ing, p. 5, Contents, ed. 1853.) 

130. The subjoined illustrates Mode, Man- 
ner, and the idea of " leading" the pupil : 

"The class were puzzled to understand the 
resistance of the various media. ' I do not 
know as I understand what media means, ' said 
one of the boys. ' A medium is that in which 
a body moves, ' read the teacher from a book. 
' A medium ? ' ' Yes ; we say medium when 
we mean but one, and media when we mean 
more than one.' After a time, the pupil still 
gaining no light, the regular teacher approached : 
' John, ' — taking his watch in his hand — 
* would this watch continue to go, if I should 
drop it into a pail of water ? ' 'I should think 
it would not long. ' * Why not ? ' ' Because 
the water would get round the wheels and 
stop it, I should think. ' ' How would it be if I 
should drop it into a quart of molasses ? ' The 
boys smiled. ' Or into a barrel of tar ? ' ' Sup- 
pose I should force it, while open, into a quantity 
of lard.' John said, ' The watch would not go 
in any of the articles.' ' Articles, why not 
say Media?' ' Oh, I understand it now.' " 
\lhicL, pp. 319-321.) 

131. In the annexed extract, the author uses 
" Manner" properly, but substitutes Method for 
Mode : " The agreeable talents are too much 
confined to method. They are rendered too ab- 
stracted by being reduced to maxims and pre- 



METHODS OF TEACHING. 123 

cepts ; and hence those things which should 
constitute the amusement of young people, are 
made disgusting to them, as the study of an art. 
I cannot conceive any thing more ridiculous, than 
to see an old singing or dancing-master, approach 
a young, lively, giggling girl, with a frigid and 
formal air ; and assume, in teaching his frivolous 
science, a more pedantick and magisterial tone, 
than if he were teaching her the catechism. Is 
it that the art of singing, for instance, depends 
on the knowledge of written musick ? Is it not 
possible to acquire a just command of voice, to 
learn to sing with taste, and even to accompany 
an instrument, without knowing a single note ? 
Is the same manner of singing adapted to all 
voices ? Doth the same method of teaching 
suit equally every genius ? It is impossible to 
make me believe, that the same attitudes, the 
same steps, the same motions and gestures, or 
even the same dances, are equally proper for a 
little, lively, sharp-eyed brunette, and a tall 
beauty with languishing eyes and flaxen hair. 
When I see a dancing-master give the same les- 
son, therefore, indiscriminately to both, I say 
to myself, this man follows the customs of his 
profession, but he understands nothing of his 
art." (Rousseau, ^milius, vol. 3, p. 205, ed. 
1783, London.) 

132. In the extract following, the Socratic 
Mode, often improperly called Method, is illus- 
trated : " Now a guide, when he has found a 
man out of the road leads him into the right 
way : he does not ridicule or abuse him and 



124 OK THE THEORY OF 

then leave him. Do you also show the illiterate 
man the truth, and you will see that he follows. 
But so long as you do not show him the truth, 
do not ridicule him, but rather feel your own 
incapacity. How then did Socrates act ? He 
used to compel his adversary in disputation to 
bear testimony to him, and he wanted no other 
witness. Therefore he could say, * I care not 
for other witnesses, but I am always satisfied 
wdth the evidence (testimony) of my adversary, 
and I do not ask the opinion of others, but only 
the opinion of him who is disputing with me.' 
For he used to make the conclusions drawn 
from natural notions so plain that every man saw 
the contradiction (if it existed) and withdrew 
from it (thus): Does the envious man rejoice? 
By no means, but he is rather pained. AVell, do 
you think that envy is pain over evils ? and 
what envy is there of evils ? Therefore he made 
his adversary say that envy is pain over good 
things. Well then, would any man envy those 
who are nothing to him ? By no means. Thus 
having completed the notion and distinctly 
fixed it he would go away without saying to his 
adversary, Define to me envy ; and if the ad- 
versary had defined envy, he did not say, You 
have defined it badly, for the terms of the defi- 
nition do not correspond to the thing defined — 
These are technical terms, and for this reason 
disagreeable and hardly intelligible to illiterate 
men, which terms we (philosophers) cannot lay 
aside. But that the illiterate man himself, who 
follows the appearances presented to him, should 



METHODS OF TEACHING. 125 

be able to concede any thing or reject it, we can 
never by the use of these terms move him to 
do. Accordingly being conscious of our own 
inability, we do not attempt the thing ; at least 
such of us as have any caution do not. But the 
greater part and the rash, when they enter into 
such disputation, confuse themselves and con- 
fuse others ; and finally abusing their adver- 
saries and abused by them, they walk away. 

" Now this was the first and chief peculiarity 
of Socrates, never to be irritated in argument, 
never to utter any thing abusive, any thing insult- 
ing, but to bear with abusive persons and to put 
an end to the quarrel. If you would know what 
great power he had in this way, read the Sym- 
posium of Xenophon, and you will see how many 
quarrels he put an end to. Hence with good 
reason in the poets also this power is most highly 
praised, 

' Quickly with skill he settles great disputes. ' 
Hesiod, Tlwogony, v. 87. 

Well then ; the matter is not now very safe, 
and particularly at Rome ; for he who attempts 
to do it, must not do it in a corner, you may be 
sure, but must go to a man of consular rank, if 
it so happen, or to a rich man, and ask him. 
Can you tell me. Sir, to whose care you have 
entrusted your horses ? — By all means. — Well 
then ; can you tell me to whom you entrust 
your gold or silver things or your vest- 
ments ? I don't entrust even these to any one 
indifferently. Well ; your own body, have you 



126 ON" THE THEORY OF 

already considered about entrusting tlie care 
of it to any person ? — Certainly. — To a man 
of experience, I suppose, and one acquainted with 
the aliptic, or with the healing art ? — With- 
out doubt. — Are these the best things that you 
have, or do you also possess something else 
which is better than all these ? — What kind of 
a thing do you mean ? — That I mean which 
makes use of these things, and tests each of 
them, and deliberates. — Is it the soul that you 
mean ? — You think right, for it is the soul 
that I mean. — In truth I do think that the 
soul is a much better thing than all the others 
which I possess. — Can you then show us in 
what way you have taken care of the soul ? for 
it is not likely that you, who are so wise a man 
and have a reputation in the city, inconsiderately 
and carelessly allow the most valuable thing that 
you possess to be neglected and to perish. — 
Certainly not. — But have you taken care of 
the soul yourself ; and have you learned from 
another to do this, or have you discovered the 
means yourself ? — Next, if you persist in troub- 
ling him, there is danger that he may raise his 
hands and give you blows. I was once myself 
also an admirer of this mode of instruction until 
I fell into these dangers." (Epictetus, Dis- 
courses, chap, xii.) 

133. In the following extract the conceptions 
of Mode and Manner of Teaching are not dis- 
tinguished from that of Methods of Teaching. 
*' Another ' peccant humour ' which at present 
infects the body of education is the employment 



METHODS OF TEACHIi^G. 127 

of Mechanical Methods. These methods were 
perhaps not at first mechanical ; they have be- 
come so by degeneration in the hands of merely 
imitative persons. If a method is not thoroughly 
assimilated by the teacher so as to become a liv- 
ing part of his own mind, if it does not marry 
itself willingly to his own thought and his own 
habits, if it is adopted as a mere plan for saving 
himself trouble and for escaping from his usual 
amount of work, it has a tendency to degenerate 
into a kind of machine, into something that 
cannot call forth thought and mental activity from 
his pupils. The essential requisite of a method 
is that it shall be living and possess the adapta- 
bility of life, and that it shall not interfere with 
but promote the spontaneous interest which the 
pupil may be inclined to feel in his subject. But 
our ancient and standing enemy — routine — is at 
hand here also, and is always ready to turn the 
best method into a monotonous device, or a crank- 
like exercise of activities. Man is by nature a 
hunting animal, and the heuristic method in 
teaching is one of the most potent for developing 
the mental pov/ers. But in the degeneration 
which is natural to all human things, unless the 
breath that created them at first breathes through 
them again, among the destructive powers which 
produce this degeneration, there is none more 
potent than the habit of imitation. Question 
and answer — from the pupil as well as from the 
teacher — is one of the best ways of searching out 
truth that are given to human faculties. But no 
sooner is this perceived than some one writes a 



128 OIT THE THEORY OF 

book on wliat lie calls this method, and the life 
is killed out of the method by the very process 
which seemed to preserve it — it is strangled in 
the grasp of stereotype. And there are now 
hundreds of books, used mostly in ladies' schools, 
in which this base-born plan is still followed, to 
the irretrievable loss of those who are subjected 
to the process. An eminent Cambridge mathe- 
matician at present trains all his pupils on this 
heuristic method — and without book ; and his 
success at the university as well as in school is 
marked and solid. But if he were to give a 
sketch of his method in writing, it would be ig- 
nobly stuck to and slavishly followed — to the 
death of the very method he had been endeavour- 
ing to set forth and recommend. If we could 
only train all our teachers to the use and constant 
practice of the heuristic method, we should make 
them themselves more strong in thought and 
purpose, more firm and real in their intellectual 
life, and more capable of firing their pupils with 
a single and undivided zeal for truth. . . . 
We are in fact overdone with machinery ; our 
education is choked by the means we use to 
promote it ; and the informing spirit is too often 
absent. . . . 

"... Our mechanical methods blind us to 
the necessity of seeking to analyse our subjects in 
the fullest manner, and so to arrange the steps 
that the children may go up with ease and plea- 
sure. We are constantly giving knowledge 
prematurely ; we are every day anticipating re- 
sults which the child will reach for himself ; and 



METHODS OF TEACHIKG. 129 

all over our pupils suffer in their brains from tlie 
malady of the day — imperfect digestion." (Mei- 
klejohfij Inaug. Address, Bell Chair of Educatiorij 
pp. 33-36, 1876.) 

" 134. The expressions " Methods of Nature," 
'• Nature's Methods," ' ' Consult Nature for 
Methods of Education and Teaching, ' ' are heard 
from time to time. It may be profitable to ex- 
amine this conception a little. What is Nature ? 
How does she work ? Where shall we find her ? 
We find her about us everywhere, as a wild, in- 
congruous, heterogeneous, restless mass of objects 
and activities. The most natural things in the 
world, probably, are a swamp and barbarism, for 
they are "fresh from the hand of Nature." 
The most natural road across the swamp is a 
corduroy road. The most natural action of a 
boy is to kick another boy when he dislikes 
him. The most natural way to occupy land is 
to tent upon it, and by force keep others away 
from it, as the nomadic peoples do. The most 
natural of plows is the Asiatic — the fork of a 
tree. The most natural apple is that which 
grows from the natural seed, not the welcome 
fruit of the graft. We also say that these works 
of art, all high art, are natural. What, then, is 
Nature ? Nature is not simply the fact that is 
presented to man — she is not alone an object 
formed without the help of man — she is not a 
single objective thing by itself. Nature is a 
term for Capacities and Possibilities, whether 
of matter or of mind. We speak of capacities 
of the human mind, all of which are natural ; 



130 OK THE THEORY OF 

and the developments of tliem are all natural. 
Nothing can be produced which is outside of 
the range of possibilities, and, hence, that is 
outside of Nature. But by way of distinc- 
tion, those things which man himself has been 
instrumental in directing and controlling are 
called Artificial. If the swamp and the barba- 
rian are very natural, drained meadows and civ- 
ilization are very artificial. Yet in all these 
cases man never can go beyond what his own 
natural powers can naturally do. No man ever 
constructs a bridge or paints a madonna that his 
natural powers do not naturally accomplish. 
It is all of Nature, and all natural — just as natural 
as it was for Demosthenes to stammer or, subse- 
quently, to move all Greece by his eloquence. 
One man uses his right hand familiarly, another 
his left, and still another both with equal facility 
— which is the natural one ? An Icelander natu- 
rally resists cold — an African naturally resists 
heat — an American resists both heat and cold. 
Which is the natural case ? A honey bee gath- 
ers honey in temperate zones, but, moved south- 
ward, ceases — what is the naturalness in the 
case ? In these cases one is just as natural as 
another — they all are so because of native en- 
dowments, capacities, or possibilities. What is 
the most natural language to speak, for a child, 
English, French, or Italian ? ' ' Man, by nature, 
is formed to suffer with patience, and die in 
peace. It is the physicians with their prescrip- 
tions, the philosophers with their precepts, and 
the clergy with their prayers and exhortations, 



METHODS OF TEACHIN"G. 131 

that have debased the heart of man, and made 
him ignorant how to die." (Rousseau, Emilius, 
vol. 1, p. 47.) In the following, which is the 
natural stage of relationship, compared to that 
now established by law and custom in the United 
States at the present time ? " We shall endeavour 
to establish the following propositions : — 1. That 
the most ancient system in which the idea of 
blood-relationship was embodied, was the system 
of kinship through females only. 2. That the 
primitive groups were, or were assumed to be, 
homogeneous. 3. That the system of kinship 
through females only tended to render the exo- 
gamous groups heterogeneous, and thus to super- 
sede the system of capturing wives. 4. That 
in the advance from savagery the system of 
kinship through females only was succeeded by 
a system which acknowledged kinship through 
males also ; and which, in most cases, passed 
into a system which acknowledged kinship 
through males only. 5. That the system of kin- 
ship through males tended to rear up homoge- 
neous groups, and thus to restore the original 
condition of affairs — where the exogamous preju- 
dice survived — as regards both the practice of 
capturing wives and the evolution of the form 
of capture. 6. That a local tribe, under the 
combined influence of exogamy and the system 
of female kinship, might attain a balance of per- 
sons of different sexes regarded as being of 
different descent, and that thus its members might 
be able to intermarry with one another, and 
wholly within the tribe, consistently with the 



132 OIsT THE THEORY OF 

principle of exogamy. 7. That a local tribe, 
having reached this stage and grown proud 
through success in war, might decline intermar- 
riage with other local tribes and become a caste. 
8. That on kinship becoming agnatic, the mem- 
bers of such a tribe might yield to the universal 
tendency of rude races to eponomy, and feign 
themselves to be all derived from a common an- 
cestor, and so become endogamous. And 9. 
That there is reason to think that some endo- 
gamous tribes became endogamous in this same 
manner. . . . The earliest human groups can have 
had no idea of kinship. . . . The idea must be re- 
garded as a growth. . . . Individuals had been 
affiliated not to persons, but to some group. . . . 
As distinguished from men of other groups, 
they would be the group-stock, and named after 
the group." (McLennan, Primitive Marriage, 
pp. 118-123, ed. 1876, London.) 

135. The question is really, not what is nat- 
ural ? but what is artificial ? If the word has 
any proper signification and scope, they must be 
something like this : — Artificial things include 
all those products and results which have been 
developed from the capacities and possibilities of 
Nature by the direct agency of man. Under 
this definition come all that man has ever done 
in civilization and in history — i.e., in civilization. 
" Culture or Civilization, taken in its wide eth- 
nographic sense, is that complex whole which in- 
cludes knowledge, belief" (religious and other- 
wise), " art, morals, law, custom, and any other 
capabilities and habits acquired by man as a mem- 



METHODS OF TEACHIN^G. 133 

ber of society. ' ' (Tylor, Primitive Culture, vol. 
i., p. 1, ed. 1874, New York.) In so far as the 
faculties of the mind are native to the mind, they 
are natural — but in so far as they are developed 
into power by this or that kind of life, or by 
this or that branch of knowledge, and for this or 
that purpose, the developed powers and the re- 
sulting products of effort, although quite natural, 
are known as at'tificial. Methods of Educa- 
tion are artificial. Modes of Teaching are arti- 
ficial, yet, if based upon principles, they are na- 
turally founded upon the native powers of the 
learning mind and the subject-matter to be learned. 
This subject-matter is both natural and artificial, 
although all produced by the capacities of Na- 
ture. Methods of Teaching, being founded upon 
the innate nature of things, are natural. 

136. It is also true that the term " natural," 
as commonly understood when applied to the 
human conditions, means the general idea or no- 
tion that people acquire as an induction from 
experience. An action is pronounced natural in 
proportion as it approaches spontaneous favor 
from the greatest number of observers. In pro- 
portion as it diverges from this it is called 
" affected," " false," '' sham," '' unnatural," 
" monstrous." Still all these phases of experi- 
ence and observation are within the capacities of 
Nature, and hence natural. A broad discrimi- 
nation should be made between the term natural 
as applied to one individual, and as applied in 
the sense of the inductive general idea. The 
author who can gather up the sense of the 



134 Oiq" THE THEORY OF 

greatest number of people into one picture or 
character, or trait of experience, is called the 
most life-like and natural in his writings. But 
he is no more natural than the man who stam- 
mers, or squints, or says, as the child, " I be 
going. ' ' 

137. *' But the only distinct meaning of that 
word (natural) is, stated, fixed, or settled ; since 
what is natural as much requires and presup- 
poses an intelligent agent to render it so, i.e. to 
effect it continually, or at stated times, as what 
is supernatural or miraculous does to effect it 
once." (Butler, Analogy, Malcom's ed., 1860, 

138. " According to its derivation, nature 
(natura — nascitur) means that which is born or 
produced — the becoming ; that which has a be- 
ginning and an end ; that which has not the 
cause of its existence in itself, and the cause of 
which must be sought in something antecedent 
to and beyond itself — that is, nature is the phe- 
nomenal. This the word expresses in the strong- 
est manner. That which begins to be, as the nec- 
essary consequence of antecedent conditions, is 
natural. The co-existence, resemblance, and 
succession of phenomena constitute the order of 
nature ; and the uniformity of these relations 
among phenomena are the laws of nature. . . . 
The word ' nature ' is also employed to denote 
the essential properties of matter, and the vari- 
ous forms of energy, potential and kinetic." 
(Cocker, Theistic Conception of the World, pp. 
193-4, ed. 1875.) 



METHODS OF TEACHING. 135 

139. " Nature is the aggregate or totality of 
all material or physical plieuomena. A Law of 
Nature is the statement of a certain uniformity 
observed in the relations among phenomena. The 
laws of nature are ' simply expressions of phe- 
nomenal uniformities, having no coercive power 
whatever.' (Carpenter.) 

140. " The Uniformity of the Order of Na- 
ture may mean either ' uniformity of co-exist- 
ence ' or ' uniformity of succession. ' ' Uniformity 
of CO -existence ' means that the same substances 
must always have the same essential properties 
and the same permanent relations to other sub- 
stances. . . . The constancy of the course, 
of nature or the uniformity of causation is not a 
self-evident and necessary truth. In so far as it 
is a scientific truth it is purely an induction from 
experience, an experience which is necessarily 
limited, and therefore does not warrant a uni- 
versal conclusion. . . . It is an immediate 
fact of consciousness that the will is a cause 
which is adequate to the production of a diver- 
sity of effects. . . . Physical science itself 
does not teach that the course of nature is abso- 
lutely uniform. . . . ' Nature,' says Dr. 
Cohn, of Breslau, ' is an equation with very 
many unknown quantities. It is the work of 
natural science to determine the value of these 
quantities.' " [IJjkL, pp. 325-33.) 

141. " According to its derivation, nature 
should mean that which is produced or born ; 
but it also means that which produces or causes 
to be born. . . . The term nature is used 



136 02^ THE THEOKY OF 

sometimes in a wider, sometimes in a narrower 
extension. When employed in its most exten- 
sive meaning, it embraces the two worlds of 
mind and matter. When employed in its more 
restricted signification, it is a synomym for the 
latter only, and is then used in contradistinction 
to the former. In the Greek philosophy, . . . 
the word was general in its meaning ; and in- 
cluded not only the sciences of matter, but also 
those of mind. AVith us, the term nature is 
more vaguely extensive than the terms physics, 
physical, physiology, or even than the adjective 
natural ; whereas, in the philosophy of Germany, 
natur and its correlatives, . . . are, in gen- 
eral, expressive of the world of matter in contrast 
to the world of intelligence. 

"Nature as opposed to art, all physical 
causes, all the forces which belong to physical 
beings, organic or inorganic. The nature or es- 
sence of any particular being or class of beings, 
that which makes it what it is. 

" ' The word nature has been used in two 
senses, — viz., actively and passively ; energetic 
(= forma formans), and material (= forma 
formata). In the first it signifies the inward 
principle of whatever is requisite for the reality 
of a thing as existent ; while the essence, or es- 
sential property, signifies the inner principle of 
all that appertains to the possibility of a thing. 
Hence, in accurate language, we say the essence 
of a mathematical circle or geometrical figure, 
not the nature, because in the conception of 
forms, purely geometrical, there is no expression 



METHODS OF TEACHING. 137 

or implication of their real existence. In the 
second or material sense of the word nature, we 
mean by it the sum total of all things, as far as 
they are objects of our senses, and consequently 
of possible experience — the aggregate of phe- 
nomena, whether existing for our outer senses, or 
for our inner sense. The doctrine concerning 
nature, would therefore . . be more properly 
entitled phenomenology, distinguished into its 
two grand divisions, somatology (= doctrine of 
the general properties of bodies or material sub- 
stances), and psychology. ' (^Coleridge.) 

" * There is no such thing as what men com- 
monly call the course of nature, or the power of 
nature. The course of nature, truly and prop- 
erly speaking, is nothing else but the will of 
God producing certain effects in a continued, 
regular, constant, and uniform manner ; which 
course or manner of acting, being in every move- 
ment perfectly arbitrary, is as easy to be altered 
at any time as to be preserved.' {Clarice.) 

*' ' All things are artificial,' said Sir Thomas 
Browne, ' for nature is the art of God. ' The 
antithesis of nature and art is a celebrated doc- 
trine in the peripatetic philosophy. Natural 
things are distinguished from artificial, inasmuch 
as they have, what the latter are without, an in- 
trinsic principle of formation. (Arist.) 

" Dr. Reid said that nature is the name we 
give to the efficient cause of innumerable effects 
Avhich fall daily under observation. But if it be 
asked what nature is ? whether the first universal 
cause or a subordinate one ? whether one or 



138 ON THE THEOEY OF 

many ? whether intelligent or unintelligent ? — 
upon these points we find various conjectures 
and theories, but no solid ground upon which 
we can rest. And I apprehend the wisest men 
are they who are sensible that they know noth- 
ing of the matter. " (Fleming, Vocab. of Phil.) 
, 142. " When he was visited by one of the 
magistrates, Epictetus inquired of him about 
several particulars, and asked if he had children 
and a wife. The man replied that he had ; and 
Epictetus inquired further, how he felt under 
the circumstances. Miserable, the man said. 
Then Epictetus asked. In what respect, for men 
do not marry in order to be wretched, but rather 
to be happy. But I, the man replied, am so 
wretched about my children that lately, when 
my little daughter was sick and was supposed 
to be in danger, I could not endure to stay with 
her, but I left home till a person sent me news 
that she had recovered. Well then, said Epic- 
tetus, do you think that you acted right ? I 
acted naturally, the man replied. But convince 
me of this that you acted naturally, and I will 
convince you that everything which takes place 
according to nature takes place rightly. This is 
the case, said the man, with all or at least most 
fathers. I do not deny that : but the matter 
about which we are inquiring is whether such be- 
haviour is right ; for in respect to this matter we 
must say that tumours also come for the good 
of the body, because they do come ; and gene- 
rally we must say that to do wrong is natural, 
because nearly all or at least most of us do wrong. 



METHODS OF TEACHING. 139 

Do you sliow me tlien how your behaviour is nat- 
ural. I cannot, lie said ; but do you show me 
how it is not done according to nature, and is 
not rightly done." (Epictetus, Discourses, Book 
I., Chap. XL, Long's trans.) 

143. " The object of what we commonly 
call education — that education in which man in- 
tervenes and which I shall distinguish as artificial 
education — is to make good these defects in 
Nature's methods ; to prepare the child to re- 
ceive Nature's education, neither incapably nor 
ignorantly, nor with wilful disobedience ; and to 
understand the preliminary symptoms of her dis- 
pleasure, without waiting for the box on the ear. 
In short, all artificial education ought to be an 
anticipation of natural education. And a liberal 
education is an artificial education, which has 
not only prepared a man to escape the great evils 
of disobedience to natural laws, but has trained 
him to appreciate and to seize upon the rewards, 
which Nature scatters with as free a hand as her 
penalties. . . . Ignorance is visited as 
sharply as wilful disobedience — incapacity meets 
with the same punishment as crime. ' ' (Huxley, 
Lay SermonSj^ p. 34, ed. 1870.) 



II. 



ON THE PRACTICE OF METHODS OF 
TEACHING. 

(a) on the knowing faculties of the mind. 

144. In discussing these Elements of Meth- 
ods of Teaching, no attempt is made to present 
a systematic view of Psychology. To do this 
would require a volume by itself, and must be 
reserved for another occasion as opportunities 
shall permit. Sufficient data are introduced to 
serve as bases for Methods of Teaching. With- 
out endeavoring to classify the matter inserted, 
it is used as it best serves the scope of the inves- 
tigation. This matter is also very valuable to 
the student for its suggestiveness, even when it 
does not bear directly upon the line of the in- 
quiry. Those professional students, who are al- 
ready familiar with some system of Psychology, 
will need to be delayed only a short time on this 
division of the volume. 

145. Adapting from Sir William Hamilton's 
Metajihysics, Murray's text, edition of 1874, pp. 
39-66, psychological phenomena of conscious- 
ness are classified under three great divisions : 
(1) Cognitions, or the faculties which have the 



OF THE MliTD. 141 

power to know ; (2) Feelings, or sensibilities, 
those wliich are susceptible of giving pain or 
pleasure ; (3) Conations, which are " tendencies 
to action, and are divisible into classes, as such 
tendencies are either blind and fatal, or deliberate 
and free. The former are desires, the latter, 
volitions, (p. 226). For present purposes it is 
necessary to elaborate only the first division, 
cognitions, including consciousness. 

146. («) ''Consciousness is the recognition 
by the thinking subject of its own acts or affec- 
tions. It is an actual and not a potential knowl- 
edge. It is an immediate, not a mediate knowl- 
edge. It supposes a contrast, a discrimination 
— as the ego and non-ego, the discrimination of 
states or modifications of the internal subject or 
self from each other, and the distinction be- 
tween the parts and qualities of the outer world. 
It involves judgment, or the mental act by 
which one thing is afiirmed or denied of an- 
other. It is conditioned upon memory, for 
without this our mental states could not be held 
fast, compared, distinguished from each other, 
and referred to self. Consciousness in its sim- 
plicity necessarily involves three things, — (1.) a 
recognizing or knowing subject, ego ; (2.) a 
recognized or known modification ; and (3.) a 
recognition or knowledge by the subject of the 
modification (pp. 39-42). 

(6) " Comparison requires a tertium quid, a 
locus — call it what you will — in which the two 
outward existences may meet on equal terms. 
This forum is what is known as a consciousness. 



142 OK THE KNOWIIfG FACULTIES 

Even sensations cannot be supposed, simply as 
such, to be aware of tlieir relations to eacli other. 
A succession of feelings is not (as James Mill 
reiterates) one and the same thing with a feeling 
of succession, but a wholly different thing. The 
latter feeling requires a self -transcendency of 
each item, so that each not only is in relation, 
but knows its relation, to the other. This self- 
transcendency of data constitutes the conscious 
form. Where we suppose it to exist we have 
mind ; wliere mind exists we have it. . . , 
Thus, then, the words Use, Advantage, Interest, 
Good, find no application in a world in which no 
consciousness exists. Things there are neither 
good nor bad ; they simply are or are not. Ideal 
truth to exist at all requires that a mind also ex- 
ist which shall deal with it as a judge deals with 
the law, really creating that which it professes 
only to declare. . . . This category (of 
consciousness, or personality) might be defined 
as the mode in which data are brought together 
for comparison with a view to choice. Both 
these points, comparison and choice, will be 
found alike omnipresent in the different stages 
of its activity. The former has always been rec- 
ognized ; the latter less than it deserves. Many 
have been the definitions given by psychologists 
of the essence of consciousness. One of the most 
acute and emphatic of all is that of Ulrici, who 
in his Leib unci Seele and elsewhere exactly re- 
verses the formula of the reigning British school, 
by calling consciousness a discriminating activity. 
But even Ulrici does not pretend that conscious- 



OF THE MIN"D. 143 

ness creates the differences it becomes aware of 
in its objects. They pre-exist and consciousness 
only discerns them ; so that after allUlrici's defi- 
nition amounts to little more than saying that 
consciousness is a faculty of cognition — a rather 
barren result, I think we nmy go farther and 
add that the powers of cognition, discrimination 
and comparison which it possesses, exist only for 
the sake of something beyond themselves, name- 
ly. Selection. Whoever studies consciousness, 
from any point of view whatever, is ultimately 
brought up against the mystery of interest and 
selective attention. There are a great many 
things which consciousness is in a passive and 
receptive way by its cognitive and registrative 
powers. But there is one thing which it does, 
su9. sponte, and which seems an original peculi- 
arity of its own ; and that is, always to choose 
out of the manifold experiences present to it at 
a given time some one for particular accentua- 
tion, and to ignore the rest. And . . from its 
simplest to its most complicated forms, it exerts 
this function with unremitting industry. ' ' (James, 
Article in Mind, No. XIIL, January, 1879, pp. 
6-9.) 

147. "I. In the first place, as we are en- 
dowed with a faculty of Cognition, or Conscious- 
ness in general, and since it cannot be maintained 
that we have always possessed the knowledge 
which we now possess, it will be admitted that 
we must have a faculty of acquiring knowledge. 
But this acquisition of knowledge can only be 
accomplished by the immediate presentation of a 



144 OK THE KNOWING FACULTIES 

new object to consciousness ; in other words, by 
the reception of a new object within the sphere 
of our cognition. We have thus a faculty which 
may be called the Acquisitive, or the Presenta- 
tive, or the Receptive. Now, new or adventi- 
tious knowledge may be either of things external 
or of things internal. If the object of knowledge 
be external, the faculty receptive or presentalive 
of the qualities of such object will be a conscious- 
ness of the non-ego. This has obtained the 
name of External Perception, or of Perception 
simply. If, on the other hand, the object be 
internal, the faculty receptive or presentative of 
the qualities of such subject-object, will be a 
consciousness of the ego. This faculty obtains 
the name of Internal or Reflex Perception, or 
of Self-consciousness. By the foreign psychol- 
ogists this faculty is termed also the Internal 
Sense." (Hamilton.) 

" The two classes of sense-perceptions thus 
characterized are the original and the acquired. 
They are thus defined : an original perception is 
one that is performed by a single sense, when 
exercised alone. Whatever the mind knows in 
this way, either of an object or of its relations, 
is known directly and by an original endowment 
of man. It is a pure work or operation of na- 
ture, and cannot be traced to art. An acquired 
perception is one which we gain by experience or 
exercise. We use the knowledge given directly 
by one sense, as the sign or evidence of the 
knowledge which we might, but do not, in this 
particular case, gain by another." (Porter, 



OF THE MIND. 145 

The Human Intellect, p. 159, ed. 1869.) Con- 
tinuing from Hamilton : — 

148. " 11. In the second place, inasmuch 
as we are capable of knowledge, we must be en- 
dowed not only with a faculty of acquiring, but 
with a faculty of retaining or conserving it when 
acquired. We have thus, as a second necessary 
faculty, one that may be called the Conserva- 
tive or Retentive. This is Memory, strictly so 
denominated. 

149. " III. But, in the third place, if we 
are capable of knowledge, it is not enough that 
we possess a faculty of acquiring, and a faculty 
of retaining it in the mind, but out of conscious- 
ness. We have a reproductive power. This Re- 
productive faculty is governed by the laws which 
regulate the succession of our thoughts, — the 
laws, as they are called, of Mental Association. 
If these laws are allowed to operate without the 
intervention of the will, this faculty may be 
called Suggestion, or Spontaneous Suggestion ; 
— whereas, if appUed under the influence of the 
will, it will properly obtain the name of Remin- 
iscence, or Recollection. By reproduction, it 
should be observed, that I strictly mean the pro- 
cess of recovering the absent thought from un- 
consciousness, and not its representation in con- 
sciousness. 

150. " IV. In the fourth place, as capable 
of knowledge, we must not only be endowed with 
a presentative, a conservative, and a reproductive 
faculty ; there is required for their consummation 
a faculty of representing in consciousness, and 



146 0^ THE K2^0WIN"G FACULTIES 

of keeping before tlie mind tlie knowledge pre- 
sented, retained, and reproduced. We have thus 
a Representative faculty ; and this obtains the 
name of Imagination or Phantasy. 

151. "V. In the fifth place, all the faculties 
we have considered are only subsidiary. They 
acquire, preserve, call out, and hold up, the ma- 
terials, for the use of a higher faculty which ope- 
rates upon these materials, and which we may 
call the Elaborative or Discursive faculty. 
This faculty has only one operation, — it only 
compares. It may startle you to hear that the 
hio'hest function of mind is nothinof hio-her than 
comparison ; but, in the end, I am confident of 
convincing you of the paradox. From this mere 
act of Comparison, there are created the intellec- 
tual products known as Collective Notions, Ab- 
stractions, Generalizations, Judgments, and 
Reasoning. 

152. " VI. But, in the sixth and last place, 
the mind is not altogether indebted to experience 
for the whole apparatus of its knowledge. What 
we know by experience, without experience we 
should not have known ; and as all our experi- 
ence is contingent, all the knowledge derived 
from experience is contingent also. But there 
are cognitions in the mind which are not contin- 
gent, — which are necessary, — which we cannot 
but think, — which thought supposes as its funda- 
mental condition. These cognitions, therefore, 
are not mere generalizations from experience. 
But if not derived from experience, they must be 
native to the mind. These native cognitions are 



OF THE MIiq"D. 147 

the laws by whicli the mind is governed in its 
operations, and which afford the conditions of its 
capacity of knowledge. These necessary laws, 
or primary conditions of intelligence, are phe- 
nomena of a similar character ; and we must, 
therefore, generalize or collect them into a class ; 
and on the power possessed by the mind of mani- 
festing these phenomena we may bestow the name 
of the Regulative faculty. (Lect. on Metaph. , 
XX.) 

153. " The following is a tabular view of 
the distribution of the Special Faculties of 
Knowledge. 

COGNITIVE FACULTIES. 

I. Presentative J J- External-Perception. 

/ 2. Internal— Self -consciousness. 
II. Conservative — Memory. 

in. Eeproductive|l: ^iS^l.^'UiSnce; 
IV. Representative — Imagination or Phantasy, 
V. Elaborative — Comparison, or the Faculty of 
Relations. 
VI. Regulative — Reason or Common Sense." 

154. " Some writers on education call the 
desire of intellectual progression the faculty of 
obtaining knowledge, — that is to say, they call 
painting seeing, — or the intellectual powers, and 
think of the senses and the memory as also exert- 
ing an educational influence ; or they speak of 
the development of spontaneous activity, as if the 
will itself were not such a developing power. 
. . . The will reproduces itself only, and 
acts only within, not without, itself ; for external 



148 01^ THE KNOWING FACULTIES 

action is as little the new act of the particular vo- 
lition, as are the words signifying it of the par- 
ticular thought. The desire of mental progress, 
on the contrary, enlarges its world for the recep- 
tion of new creatures, and is as dependent on ob- 
jects as the pure will is independent of them. 
The will could reach its ideal, but finds a strange 
opposition to it, — whereas no power stands op- 
posed to thought, — but only the difference be- 
tween its steps, and the impossibility of seeing 
whither they reach. . . . The mental desire 
of advancement which, in a higher sense than 
the physical, works by means of, and in ac- 
cordance with, the will, that is to say, creates 
new ideas out of old ideas, is the distinguish- 
ing characteristic of man. No will restrains 
the order of a beast's actions. In our wak- 
ing moments we are actually conscious that 
we think ; in our dreams we receive, if I may 
so express it, that consciousness. In the man 
of genius the formation of ideas appears actually 
creative ; in ordinary men, merely recollective 
and necessary." (Richter, Levana, pp. 342-4.) 

155. " The Intelligence reaches its end ac- 
cording to a certain way, process, or method. 

The Formal movements of intelligence 
accordingly fall under two heads, thus : — (a) 
Will-power. (6) Process or Method of reaching 
Knowledge." (Laurie, Syn. of Lectures, p. 10, 
ed. ]877^.) 

156. "No act of intelligence can be per- 
formed without some determination of the Ego, 
no act of determination without some cognition, 



OF THE MIKD. 149 

and no act of the one or the other without some 
amount of feeUng being mingled in the process. 
Tims, while each mental state may have its dis- 
tinctive characteristics, there is unity at the root 
— the identical Ego, spirit, JFill (p. 36). . . . 
"When, therefore, it is asked, What causes the 
will to effect one volition rather than another ? 
our answer is. Nothing whatever ! Of its own 
effect, JFill, in its proper conditions, is not a 
partial, but a full and adequate cause. " (Cocker, 
Theistic Conception of the World, p. 391.) 

157. In continuation of what has been said 
there is added the following, adapted from Por- 
ter on the Imagination : " The imagination has 
various applications, {a) The poetic imagina- 
tion is that creative power which is employed for 
the gratification of the emotional nature in the 
production of pictures more or less elevating in 
their associations, which are fixed and expressed 
by means of rhythmical language. 

158. {h) "The philosophic imagination is 
that without which philosophic invention and 
discovery are impossible. To invent or discover, 
is always to recombine. It is to adjust in new 
positions, objects or parts of objects which have 
never been so connected before. The discoverer 
of a new solution for a problem, or a new dem- 
onstration for a theorem in mathematics, the 
inventor of a new application of a power of na- 
ture already known, or the discoverer of a power 
not previously dreamed of, the discoverer of a 
new argument to prove or deduce a truth or a 



150 OK THE Iv]S"OWII^G FACULTIES 

new induction from facts already accepted, the 
man who evolves a new principle or a new defi- 
nition in moral or political science — must all ana- 
lyze and recombine in the mind things, acts, or 
events, with their relations, in positions in which 
they have never been previously observed or 
thought of. This recombination is purely men- 
tal. If there be a discovery or invention, there 
has never before been such a juxtaposition of the 
materials nor of their parts in the world of fact 
or in the thoughts of men. These objects and 
parts are now for the first time brought together 
in the mind — i.e., the imagination of the dis- 
coverer. Every discovery is, in fact, a work of 
the creative imagination. ... In the com- 
munication of scientific truth there can be no ques- 
tion that a large measure of imagination is of 
essential service. He that would amply illus- 
trate, powerfully defend, or effectively enforce 
the principles and truths of science, is greatly 
aided by a brilliant imagination. This, of all 
other gifts, delivers him from that tendency to the 
dry and abstract, to the general and the remote, 
to which the expounder of science is continually 
exposed from his familiarity with principles 
which are strange to his pupils and readers, and 
which need to be continually explained and illus- 
trated by fresh and various examples. The 
philosophic writer or teacher who is gifted with 
imagination is more likely to be clear in state- 
ment, ample in illustration, pertinent in his ap- 
plication and exciting in his enforcement of the 



OF THE MIKD. 151 

tratlis with which his science is conversant, what- 
ever may be the subject-matter with which the 
science is concerned. 

159. '* (c) The practical or ethical uses of 
the imagination are numerous and elevated. 
These are sufficiently obvious from the single 
consideration, that the law of duty is and must 
be an ideal law : for whether it is or is not ful- 
filled, it must precede the act which reaches or 
falls short of itself. Every ethical rule must be 
a mental creation, an ideal formed by the crea- 
tive power, and held before the soul as a guide 
and law. 

160. " (fQ The relation of the imagination to 
religious faith is interesting and important. 
The objects of our faith, by their very definition, 
have never been subjected to direct or intuitive 
knowledge. Neither sense-perception nor self- 
consciousness, have confronted them directly or 
brought report of them. And yet the imagina- 
tion pictures these objects as real and most im- 
portant. " {Human Intellect, pp. 366-73, ed. 
1869.) 

161. " The fact is, that the educated Native 
mind requires hardening. That culture of the 
imagination, that tenderness for it, which majf 
be necessary in the West, is out of place here ; 
for this is a society in which, for centuries upon 
centuries, the imagination has run riot, and 
much of the intellectual weakness and moral 
evil which afflict it to this moment, may be 
traced to imagination having so long usurped the 
place of reason. What the Native mind re- 



152 OK THE KKOWIIiTG FACULTIES 

quires, is stricter criteria of trutli ; and I look 
for the happiest moral and intellectual results 
from an increased devotion to those sciences by 
which no tests of truth are accepted, except the 
most rigid." (Maine, Village Communities,^^. 
275-6, ed. 1876, Address to University of Cal- 
cutta, March, 1866.) 

162. Concerning the subject of memory 
more should be said, because it is a faculty 
which performs so lasting and important a part 
in the existence of man. Various views of 
memory are expressed by writers who study 
Psychology ; the prevailing notion appears to be 
that it is a faculty which retains and reproduces 
in Consciousness the mental products that former- 
ly were there. Another view of memory is 
this : Memory is that endowment of the Mind by 
which it is able to reproduce its previous modi- 
fications. " Modification is properly the bring- 
ing a thing into a certain mode of existence." 
(Hamilton, Metaphysics, Murray, p. 33.) 

163. Regarding the nature of memory as a 
factor in the conception of teaching, the follow- 
ing opinions are appended : — " "With regard to 
younger boys, "he said, ' It is a great mistake to 
think that they should understand all they learn; 
for God has ordered that in youth the memory 
should act vigorously, independent of the under- 
standing — whereas a man cannot usually recollect 
a thing unless he understands it.' " (Life of Dr. 
Tho. Arnold, pp. 133-4, ed. 1870, Boston.) 

164. " Imagination, Memory, and Hope, 
are psychologically one and the same faculty. In 



OF THE MII?^D. 153 

Imagination, the presence of tlie image is neces- 
sarily accompanied by a conviction of the possi- 
ble existence of the corresponding object in an 
intuition. Memory is the presence of the same 
image, ac ^ompanied by a conviction of the fact, 
that the object represented has actually existed 
in a past intuition. Hope, in like manner, is 
the presence of the same image, together with 
an anticipation, more or less vivid, of the actual 
existence of the object in a future intuition. 
Imagination, memory, and hope, are thus 
(whether formed by a reflective process or not) in 
their actual results partly presentative, partly rep- 
resentative. They are presentative of the im- 
age, which has its own distinct existence in con- 
sciousness, irrespectively of its relation to the ob- 
ject which it is supposed to represent. They 
are representative of the object, which that im- 
age resembles, and which, either in its present 
form or in its several elements, must have been 
presented in a past act of intuition. Thus there 
is combined an immediate consciousness of the 
present with a mediate consciousness of the past. 
An immediate or presentative consciousness of 
the past or the future, as such, is impossible. 
Imagination, being representative of an intuition, 
is, like intuition, only possible on the condition 
that its immediate object should be an indi- 
vidual. ... On the other hand, my no- 
tion of a man in general can attain to univer- 
sality only by surrendering resemblance ; it be- 
comes the indifferent representative of all man- 
kind, only because it has no special likeness to 



154 OIT THE KITOWIN"G FACULTIES 

any one in particular. This distinction must be 
carefully borne in mind in comparing imagina- 
tion with the cognate process of conception. 
Memory is sometimes considered as the 
result of a process of thought." (Mansel, Meta- 
physics, pp. 128-9, ed. 1871.) 

165. " ' The resuscitation of thoughts which 
in some shape or other have previously occupied 
the mind, ' is nothing more or less than a prel- 
ude to what will unquestionably form a chief 
part of our intellectual experience of futurity ; 
namely, the inalienable and irrepressible recollec- 
tion of the deeds and feelings played forth while 
in the flesh, providing a beatitude or a' misery 
forever. Ordinarily, this resuscitation is of such 
a medley and jumbled character, that not only is 
the general product unintelligible, but the par- 
ticular incidents are themselves too fragmentary 
and dislocated to be recognised. But it is not 
always so. There must be few who have not 
experienced in their sleep, with what peculiar 
vividness, unknown to their Avaking hours, and 
with what minute exactitude of portraiture, 
events long past and long lost sight of, will not 
infrequently come back, shewing that there is 
something within which never forgets, and which 
only waits the negation of the external world, to 
leap up and certify its powers. . . . That 
which so vividly remembers is the Soul ; and if 
in the sleep which refreshes our organic nature, 
it utters its recollections brokenly and indistinct- 
ly, it will abundantly compensate itself when the 
material vesture which clogs it shall be cast 



OF THE MIKD. 155 

away. Much of the indistinctness of dreams 
probably arises from physical unhealthiness. If 
a sound body be one of the first requirements to 
a sound mind, in relation to its waking employ- 
ments, no less must it be needful to the sanity 
and precision of its sleeping ones. Brilliant as 
are the powers and functions of the spiritual 
body, the performance of them, whether sleep- 
ing or waking, so long as it is investured with 
flesh and blood, is immensely, perhaps wholly, 
contingent on the health of the material body." 
(Grindon, Life, pp. 290-291, 3d ed., London.) 

166. " Memory, a receptive, not a creative 
faculty, is subjected to physical conditions more 
than all other mental powers ; for every kind of 
weakness (direct and indirect, as well bleeding as 
intoxication) impairs it, and dreams interrupt it ; 
it is not subject to the will, is possessed by us 
in common with the beasts ; and can be most 
effectually strengthened by the physician: a bit- 
ter stomachic will increase it more than a whole 
dictionary learnt by heart. For if it gained 
strength by what it receives, it would grow with 
increasing years, that is, in proportion to its 
wealth in hoarded names ; but it can carry the 
heaviest burdens most easily in unpracticed youth, 
and it holds those so firmly that they appear 
above the gray hairs of age as the everg-reens of 
childhood." (Richter, Zemna, pp. 370-1.) . . . 

" No one has a memory for everything, be- 
cause no one feels an interest in everything. 
And the physical powers set bounds even to the 
strengthening influence of desire on the memory ; 



156 OIT THE KI^OWIi^G FACULTIES 

■ — think of that when with children, — for in- 
stance, if a Hebrew bill of exchange for a thou- 
sand pounds were promised, on condition of de- 
manding its payment in the very words of the 
document, as once read aloud, everybody would 
try to remember them, but, unless he were a 
Jew, the words and the form would fail him. 
I myself, however, would not choose 
any of these proposed methods of catching and 
yoking attention (artificial arts of memory), but 
would adopt that of steady industry. I do be- 
lieve that a rod would help a creeping child to 
walk better than crutches under his arms, which 
at first carry, but afterwards are carried by him. 
Yea yea, nay nay, are the best double watch- 
words for children. . . . Fear cripples the 
memory, both by producing physical weakness 
and mental irritation ; the frost of cold fear 
chains every living power which it approaches." 
(Richter, Levana, pp. 374-6.) 

167. " It is incomprehensible to me, how 
people fancy they can teach children to read or 
write the letters easily by pointing out their re- 
semblances, and laying before them at once i y, C 
e, or, in writing, i r, h k, &c. The very oppo- 
site plan ought to be pursued ; i should be 
placed next g, v next z, o next r ; the contrast, 
like light and shadow, make both prominent ; 
until reflected lights and half shades can separate 
them anew from each other. The fast-rooted 
dissimilarities serve at last to hold fast the re- 
semblance that exists among them. So the old 
plan of teaching spelling by lists of words alpha- 



OF THE MIN'D. 157 

betically arranged is bad, on account of tlie diffi- 
culty of distinguishing similar sounds ; whereas 
that of classing together derivations from the 
same Latin or Greek word assists the remem- 
brance, because the radical word does not alter. ' ' 
(Richter, Levana, pp. 375-6.) 

168. " There is not a man livino;, whom it 
would so little become to speak of memory as 
myself, for I have none at all ; and do not think 
that the world has again another so treacherous 
as mine. My other faculties are all very ordi- 
nary and mean ; but in this I think myself very 
singular, and to such a degree of excellence, that 
(besides the inconvenience I suffer by it, which 
merits something) I deserve methinks, to be 
famous for it. and to have more than a common 
reputation : though, in truth the necessary use 
of memory consider' d, Plato had reason when he 
call'd it a great and powerful Goddess. In my 
country, when they would decypher a man that 
has no sense, they say, such a one has no mem- 
ory." (Montaigne, Essays, p. 33, third ed., 
London.) 

169. " I am oblig'd to fortune for having so 
oft assaulted me with the same sort of weapons ; 
she forms and fashions me by usance, hardens 
and habituates me so, that I can know within a 
httle for how much I shall be quit. For want 
of natural memory, I make one of paper ; and as 
any new symptom happens in my disease, I set 
it down ; from whence it falls out, that being 
now almost past all sorts of examples, if any as- 
tonishment threaten me, tumbling over these lit- 



158 OH THE KNOWIN"G FACULTIES 

tie loose notes, as the Sibyls leaves, I never fail 
of finding matter of consolation from some fa- 
vourable prognostick in my past experience." 
{Ibid., p. 652.) 

' ' Memory is a faculty of wonderful use, and 
without which the judgment can very hardly per- 
form its office : for my part I have none at all : 
what any one will propose to me, he must do it 
b}'^ parcels, for to answer a speech consisting of 
several heads, I am not able. I could not re- 
ceive a commission by word of mouth, without 
a note-book : and when I have a speech of con- 
sequence to make, if it be long, I am reduc'd 
to the miserable necessity of getting it word for 
word what I am to say by heart ; I should other- 
wise have neither fashion nor assurance, being 
in fear that my memory would play rac a slippery 
trick. But this way is no less difficult to me 
than the other. I must have three hours to 
learn three verses. And besides, in a work of a 
man's own, the liberty and authority of altering 
the order, of changing a word, incessantly vary- 
ing the matter, makes it harder to stick in the 
memory of the author. The more I mistrust it, 
the worse it is, it serves me best by chance, I 
must negligently sollicit it, for I press it, 'tis as- 
tonish' d, and after it once begins to stagger, the 
more I sound it, the more it is perplex'd ; it 
serves me at its own hour, not at mine. And 
the same defect 1 find in my memory, I find also 
in several other parts. I fly command, obliga- 
tion and constraint. That which I can other- 
wise naturally and easily do : if I impose it upon 



OF THE MIKD. 159 

myself by an express and strict injunction, I can- 
not do it. Being once in a place where it is 
look'd upon as the greatest discourtesie imagina- 
ble not to pledge those who drink to you, 
though I had there all liberty allowed me, I 
try'd to play the good fellow, out of respect to 
the ladies that were there, according to the cus- 
tom of the country ; but there was sport 
enough, for this threatning and preparation, that 
I was to force myself contrary to my custom 
and inclination, did so stop my throat, that I 
could not swallow one drop ; and was depriv'd 
of drinking so much as to my meat. I found 
myself gorg'd, and my thirst quench' d by so 
much drink as mj imagination had swallow 'd. 
This effect is most manifest in such as have the 
most vehement and powerful imagination : but 
it is natural notwithstanding, and there is no one 
that does not in some measure find it. They 
offer' d an excellent archer, condemn' d to dye, 
to save his life, if he would shew some notable 
proof of his art, but he refused to try, fearing 
least the too great contention of his will would 
make him shoot wide, and that instead of saving 
his life, he should also lose the reputation he had 
got of being a good marks-man. A man that 
thinks of something else, will not fail to take over 
and over again the same number and measure of 
steps, even to an inch, in the place where he 
walks : but if he makes it his business to mea- 
sure and count thom, he will find that what he 
did by nature and accident, he cannot so exactly 
do by design. My library, which is of the best 



160 OK THE KNOWING FACULTIES 

sort of country libraries, is situated in a corner 
of my house ; if anything comes into my head 
that I have a mind to look on or to write ; lest I 
should forget it in but going cross the court, I 
am fain to commit it to the memory of some 
other. If I venture in speaking to digress never 
so little from my subject, I am infallibly lost, 
which is the reason that I keep myself in dis- 
course strictly close. I am forc'd to call the 
men that serve me either by the names of their 
offices, or their country ; for names are very hard 
for me to remember. I can tell indeed that 
there are three syllables, that it has a harsh 
sound, and that it begins or ends with such a let- 
ter, but that's all : and if I should live long, I 
do not think but I should forget my own name, as 
some others have done. Messela Corvinus, was 
two years without any trace of memory, which 
is also said of Georgius Trapezuntius. For 
my own interest, I often meditate what a kind 
of life theirs was, and if, without this faculty, I 
should have enough left to support me with any 
manner of ease, and prying narrowly into it, I 
fear that this privation, if absolute, destroys all 
the other functions of the soul. 

Planus rimarum sum, hac atque iliac perfluo. 
Ter. Eun. act. 1. fc. 2. 
" I'm full of chinks, and leak out every way." 

It has befall' n me more than once to forget the 
word I had three hours before given or receiv'd, 
and to forget where I had hid my purse, what- 
ever Cicero is pleas' d to say : I help myself to 



OF THE MIND. 161 

lose what I liave a particular care to lock safe up, 
* Memoria certe non modo philosoptiiam, sed om- 
nis vitse usura, omnesque artes, unamaxime con- 
tinet.' — Cicero. 'The memory is the recepta- 
cle and sheath of all science ;' and therefore 
mine being so treacherous, if I know little, I can- 
not much complain ; I know in general the names 
of the arts, and of what they treat, but nothing- 
more. I turn over books, I do not study them ; 
what I retain I do not know to be anothers, and 
is only what my judgment has made its advan- 
tage of ; discourses and imaginations in which it 
has been instructed. The author, place, words, 
and other circumstances, I immediately forget, 
and am so excellent at forgetting, that I no less 
forget my own writings and compositions than 
the rest. I am v^ery often quoted to myself, and 
am not aware of it ; and whoever should enquire 
of me where I had the verses and examples that 
I have here huddled together, would puzzle me 
to tell him, and yet I have not borrow' d them 
but from famous and known authors, not satisfy- 
ing myself that they were rich ; if I moreover 
had them not from rich and honourable hands, 
where there is a concurrence of authority as well 
as reason. It is no great wonder if my book 
run the same fortune that other books do, and if 
my memory lose what I have writ as well as what 
I have read, and what 1 give, as well as what I 
receive. Beside the defect of memory, I have 
others which very much contribute to my igno- 
rance ; I have a slow and heavy wit, the least 
cloud stops its progress, so that, for example, I 



162 OiT THE KN"OWIN"G FACULTIES 

never propos'd to it any never so easie a riddle 
that it could find out. There is not the least 
idle subtility, that will not gravel me. In games, 
where wit is requir'd, as chess, draughts, and the 
like, I understand no more but the motions of 
the men, ^vithout being capable of anything of 
design. I have a slow and perplex' d apprehen- 
sion, but what it once apprehends, it apprehends 
well, for the time it retains it." (Ibid.j pp. 404- 
406.) 

170. *' But the objection which is common- 
est, and -which most intimately concerns us here, 
is, that the knowledge communicated by the sub- 
ordinate Colleges and verified by this University 
is worthless, shallow, and superficial. The 
course of the University of Calcutta is sometimes 
said to be in fault, and it is alleged, to use a 
term at once expressive and fashionable, that it 
encourages ' cramming.' Now there are some 
things in our Calcutta course, of which I do not 
altogether approve. But it was settled after 
long discussion, shortly after I became Vice- 
Chancellor, and it would be absurd to be per- 
petually changing that which of all things ought 
to be fixed and permanent, on account of small 
defects which are, after all, disputable. I wish, 
however, to say something of the wdiole class of 
objections implied in that one word ' cram- 
ming. ' If there is anything in them, you know, 
I suppose, that they have a far wider application 
than their application to this University. They 
are constantly urged against the numerous com- 
petitive systems which are growing up in Eng- 



OF THE MIKD. 163 

land, and in particular against the system under 
which the Civil Service of India, probably the 
most powerful official body in the world, is re- 
cruited, and will be recruited. 

" The discredit which has been successfully 
attached to certain systems by this word is a 
good illustration of the power of what a famous 
writer called dyslogistic expression, or, to put it 
more simply, of giving a thing a bad name. And 
here I must say, that the habit Englishmen have 
of importing into India these common-place cen- 
sorious opinions about systems and institutions, 
is a great misfortune for the Natives. Even in 
the mouths of Eno;lishmen who invented them, 
they generally have very little meaning, for they 
are based on a mere fragment of truth ; when 
passed about among the multitude, they have 
still less ; and, at last, when exported hither, 
and repeated by the Natives in a foreign tongue, 
they have simply no meaning at all. 

" As far as I understand the word, it means 
nothing more than the rapid communication of 
knowledge, — communication, that is to say, at 
a rate unknown till recently. Some people, I 
know, would add something to the definition, 
and would say that cramming is the rapid com- 
munication of superficial knowledge ; but the 
two statements will generally be found identical, 
and that they mean by superficial knowledge, 
knowledge which has been rapidly acquired. 
The true point, the point which really has to be 
proved is, whether knowledge rapidly acquired 
is more easily forgotten than knowledge which 



164 OK THE KKOWIKG FACULTIES 

has "been slowly gained. The point is one upon 
which, to some extent, everybody can judge for 
himself or herself. I do not assert the negative, 
but I am rather surprised at the readiness with 
which the affirmative has been usually taken for 
granted ; no doubt, if it be true, it is a curious 
psychological fact, but surely there are some rea- 
sons for questioning the reality. It might plausi- 
bly be argued that knowledge slowly acquired, 
has been acquired at the cost of frequent inter- 
vals of inattention and forgetfulness. Now 
everybody knows that inattention and forgetful- 
ness tend to become habits of the mind, and it 
might be maintained that these habits would be 
likely to recur, in association wiih a subject of 
thought, even when that subject has for once 
been successfully mastered. On the other hand, 
it might be contended that knowledge rapidly 
acquired has been necessarily acquired under a 
certain strain and tension of the mental faculties, 
and that the effects of this tension are not likely 
to be so readily lost and dissipated. 

" The simple truth is, that under the strong 
stimulus applied by that system of examinations 
by which the entrance to almost every English 
profession is now barred, there has sprung up an 
active demand for knowledge of a more varied 
description than was once coveted, and above 
all, for knowledge rapidly imbibed and mastered. 
To meet this demand, a class of teachers has 
sprung up who certainly produce remarkable 
results with remarkable rapidity. I hear it said, 
that they are men of a lower order of mind and 



OF THE MIKD. 165 

accomplishment than the teachers who follow 
the old methods. It may be so ; but that only- 
renders the probability greater, that some new 
power has been brought into play." (Maine, 
Village Communities and Miscellanies, pp. 
282-5, ed. 1876, Address to Univ. of Calcutta, 
March, 1866.) 

171. "I have had some opportunity myself 
of making a comparison, and my judgment is 
decidedly in favour of the present system (of com- 
petitive examinations). I am aware that many 
persons think the matter is settled by asserting 
that all we do by our examination system, is to 
encourage cram ; but unfortunately no definition 
is given of what is reprobated by this much 
employed word. It seems to me that at least 
one very prominent tendency of the competitive 
system is extremely valuable ; namely, that of 
securing from the teacher attention to the prog- 
ress of his pupils individually." (Todhunter, 
Conjiict of Studies, ed. 1873, pp. 63-4.) 

172. '^ Fortunately, too, for the opponents 
of examination, an admirable ' cry ' has been 
found. Examination, they say, leads to ' cram,' 
and ' cram ' is the destruction of true study. 
People who know nothing- else about examination 
know well enough that it is ' cram.' The word 
has all the attributes of a perfect question-beg- 
ging epithet. It is short, emphatic, and happily 
derived from a disagreeable physical metaphor. 
Accordingly, there is not a respectable gentleman 
distributing prizes to a body of scholars at the 
end of the session, and at a loss for something to 



166 OK THE Kiq'OWIKG FACULTIES 

say, wlio does not think of this word ' cram, ' and 
proceed to expatiate on the evils of the examina- 
tion-system. 

" I intend in this article to take np the less 
popular view of the subject and say what I can 
in favour of examinations. I wish to analyse the 
meaning of the word ' cram,' and decide, if 
possible, whether it is the baneful thing that so 
many people say. There is no difficulty in see- 
ing at once that ' cram ' means two different 
things, which I call ' good cram ' and ' bad 
cram. ' A candidate, preparing for an important 
competitive examination, may put himself under 
a tutor well-skilled in preparing for that examina- 
tion. This tutor looks for success by carefully 
directing the candidate's studies into the most 
' paying ' lines, and restricting them rigorously 
to those lines. The training given may be of an 
arduous, thorough character, so that the faculties 
of the pupil are stretched and exercised to their 
utmost in those lines. This would be called 
* cram ' because it involves exclusive devotion 
to the answering of certain examination-papers. 
I call it ' good cram. ' 

" ' Bad cram,' on the other hand, consists in 
temporarily impressing upon the candidate's mind 
a collection of facts, dates, or formulae, held in a 
wholly undigested state and ready to be dis- 
gorged in the examination-room by an act of 
mere memory. A candidate, unable to appre- 
hend the bearing of Euclid's reasoning in the 
first book of his Elements, may learn the propo- 
sitions ofE by heart, diagrams, letters and all, like 



OF THE MIKD. 167 

a Sunday scholar learning the collects and gos- 
pels. Dates, rules of grammar, and the like, 
may be ' crammed ' by mnemonic lines, or by 
one of those wretched systems of artificial mem- 
ory, teachers of which are always going about. 
In such ways it is, I believe, possible to give an- 
swers which simulate knowledge, and no more 
prove true knowledge, than the chattering of a 
parrot proves intellect. 

" 1 am far from denying the existence of 
* bad cram ' of this character, but I hold that it 
can never be advantageously resorted to by those 
who are capable of ' good cram. ' To learn a 
proposition of Euclid by heart is far more labo- 
rious than for a student of moderate capacity to 
master the nature of the reasoning. It is ob- 
vious that all advantages, even in an examina- 
tional point of view, are on the side of real 
knowledge. The slightest lapse of memory in 
the bad ' crammer,' for instance the putting of 
wrong letters in the diagram, will disclose the 
simulated character of his work, and the least 
change in the conditions of the proposition set 
will frustrate his mnemonic devices altogether. 
If papers be set which really can be answered by 
mere memory, the badness is in the examiners. 

* ' Thorough blockheads may be driven to the 
worst kind of * cram, ' simply because they can 
do nothing better. Nor do the blockheads suffer 
harm ; to exercise the memory is better than to 
leave the brain wholly at rest. Some qualities 
of endurance and resolution must be called into 
existence, before a youth can go through the 



168 OK THE KN-QWIKG FACULTIES 

dreary work of learning off by heart things of 
which he has no comprehension. Nor with ex- 
aminers of the least intelligence is there any rea- 
son to fear that the best directed ' bad cram ' 
will enable a really stupid candidate to carry off 
honours and appointments due to others. No 
examination-papers even for junior candidates 
should consist entirely of ' book-work, ' such as 
to be answered by the simple reproduction of the 
words in a text-book. In every properly con- 
ducted examination, questions are, as a matter of 
course, set to test the candidate's power of ap- 
pl}'ing his knowledge to cases more or less differ- 
ent from those described in the books. More- 
over good examiners always judge answers by 
their general style as well as by their contents. 
It is really impossible that a stupid slovenly can- 
didate can by any art of ' cramming ' be enabled 
to produce the neat, brief, pertinent essay, a 
page or two long, which wins marks from the 
admiring examiners. 

" If we may judge from experience, too, ' bad 
cram ' does not pay from the tutor's point of 
view. That this is so we may learn from the 
fact that slow ignorant pupils are ruthlessly re- 
jected by the great ' coaches.' Those who have 
their reputation and their living to make by the 
success of their candidates cannot afford to waste 
their labor upon bad material. Thus it is not 
the stupid who go to the * cramming ' tutors to 
be forced over the heads of the clever, but it is 
the clever ones who go to secure the highest 
places. Long before the critical days of the 



OF THE MIKD. 169 

official examination, tlie experienced ' coacli ' se- 
lected his men almost as carefully as if he were 
making up the University boat. There is hardly 
a University or a College in the kino;dom which 
imposes any selective process of the sort. An 
entrance or matriculation examination, if it ex- 
ists at all, is little better than a sham. All com- 
ers are gladly received to give more fees and the 
appearance of prosperity. Thus it too often 
happens that the bulk of a college class consists 
of untutored youths through whose ears the 
learned instructions of the professor pass, harm- 
lessly it may be, but uselessly. Parents and the 
public have little idea how close a resemblance 
there is between teaching and writing on the 
sands of the sea, unless either there is a distinct 
capacity for learning on the part of the pupil, or 
some system of examination and reward to force 
the pupil to apply. 

' ' For these and other reasons which might be 
urged, I do not consider it worth while to con- 
sider ' bad cram ' any further. I pass on to in- 
quire whether ' good cram ' is an objectionable 
form of education. The good ' cramming ' tutor 
or lecturer is one whose object is to enable his 
pupils to take a high place in the list. With 
this object he carefully ascertains the scope of 
the examination, scrutinises past papers, and esti- 
mates in every possible way the probable charac- 
ter of future papers. He then trains his pupils 
in each branch of study with an intensity pro- 
portioned to the probability that questions will 
be asked in that branch. It is too much to as- 



170 OK THE KKOWIKG FACULTIES 

Slime tliat this training will be superficial. On 
the contrary, though narrow it will probably be 
intense and deep. It will usually consist to a 
considerable extent in preliminary examinations 
intended both to test and train the pupil in the 
art of writing answers. The great ' coaches ' at 
Cambridge in former days might be said to pro- 
ceed by a constant system of examination, oral 
instruction or simple reading being subordinate to 
the solving of innumerable problems. The main 
question which I have to discuss, then, resolves 
itself into this : — whether intense training direct- 
ed to the passing of certain defined examinations 
constitutes real education. The popular op- 
ponents of ' cram ' imply that it docs not ; I 
maintain that it does. 

" It happened that, just as I was about to write 
this article, the Home Secretary presided at the 
annual prize-distribution in the Liverpool College, 
on the 22d December, 1876, and took occasion 
to make the usual remarks about ' cram. ' He ex- 
pressed with admirable clearness the prevailing 
complaints against examinations, and I shall there- 
fore take the liberty of making his speech in 
some degree my text. * Examination is not edu- 
cation, ' he said. ' You require a great deal more 
than that. As well as being examined, you must 
be taught. ... In the great scramble for 
life, there is a notion at the present moment of 
getting hold of as much general superficial knowl- 
edge as you can. That to my mind is a fatal 
mistake. On the other hand, there is a great 
notion that if you can get through your examiaa- 



OF THE MIND. 171 

tion and * cram up ' a subject very well, you are 
being educated. That, too, is a most fatal mis- 
take. There is nothing which would, delight me 
so much, if I were an examiner, as to baffle all 
the ' cramming ' teachers whose pupils came be- 
fore me ' (laughter). 

" Let us consider what Mr. Cross really means. 
Examination, he says, is not education ; we re- 
quire a great deal more ; we must be taught as 
well as be examined. With equal meaning I 
might say, ' Beef is not dinner ; we want a great 
deal more ; we must have potatoes, bread, pud- 
ding, and the like. ' Nevertheless beef is a prin- 
cipal part of dinner. Nobody, I should think, 
ever asserted or imagined that examination alone 
was education, but I nevertheless hold that it is 
one of the chief elements of an effective educa- 
tion. As Mr. Cross himself said in an earlier 
part of his speech, ' the examination is a touch- 
stone and test which shows the broad distinction 
between good and bad. . . . You may 
manage to scramble through your lessons in the 
' half, ' but I will defy you to get through your 
examinations if you do not know the subjects. ' 

" Another remark of Mr. Cross leads me to 
the main point of the subject. He said — ' It is 
quite necessary in the matter of teaching that 
whatever is taught must be taught well, and noth- 
ing that is taught well can be taught in a hurry. 
It must be taught not simply for the examination, 
but it must sink into your minds, and stay there 
for life.' Both in this and his other remarks 
Mr. Cross commits himself to the popular but 



172 OK THE KN^OWIKG FACULTIES 

wholly erroneous notion that what boys learn at 
school and college should be useful knowledge 
indelibly impressed upon the mind, so as to 
stay there all their lives, and be ready at their 
fingers' ends. The real point of the objections 
to examination commonly is, that the candidate 
learns things for the examination only, which, 
when it is safely passed, he forgets again as 
speedily as possible. Mr. .Cross would teach so 
deliberately and thoroughly that the very facts 
taught could not be forgotten, but must ever af- 
ter crop up in the mind whatever we are doing. 
I hold that remarks such as these proceed from a 
wholly false view of the nature and purposes of 
education. It is implied that the mind in early 
life is to be stored with the identical facts, and 
bits of knowledge which are to be used in after 
life. It is, in fact, Mr. Cross and those who 
think with him, who advocate a kind of ' cram, ' 
enduring it is true, but still ' bad cram. ' The 
true view of education, on the contrary, is to 
regard it as a course of training. The youth in 
a gymnasium practises upon the horizontal bar, 
in order to develop his muscular powers general- 
ly ; he does not intend to go on posturing upon 
horizontal bars all through life. School is a place 
where the mental fibres are to be exercised, 
trained, expanded, developed, and strengthened, 
not ' crammed ' or loaded with ' useful knowl- 
edge. ' 

" The whole of a youth's subsequent career is 
one long course of technical ' cramming ' in which 
any quantity of useful facts are supplied to him 



OF THE MIKD. 173 

nolens volens. The merchant gets his technical 
knowledge at the clerk's desk, the barrister in 
the conveyancer's offices or the law courts, the 
engineer in the workshop and the field. It is 
the very purpose of a liberal education, as it is 
correctly called, to develop and train the plastic 
fibres of the youthful brain, so as to prevent them 
taking too early a definite ' set, ' which will after- 
wards narrow and restrict the range of acquisition 
and judgment. I will even go so far as to say 
that it is hardly desirable for the actual things 
taught at school to stay in the mind for life. 
The source of error is the failure to distinguish 
between the form and the matter of knowledge, 
between the facts themselves and the manner in 
which the mental powers deal with facts. 

" It is wonderful that Mr. Cross and those who 
moralise in his strain do not perceive that the ac- 
tual facts which a man deals with in life are infi- 
nite in number, and cannot be remembered in a 
finite brain. The psychologists, too, seem to me 
to be at fault in this matter, for they have not 
sufficiently drawn attention to the varying degrees 
of duration required in a well organised memory. 
We commonly use the word Memory so as to 
cover the faculties of Retention, Reproduction 
and Representation, as described by Hamilton, 
and very little consideration will show that in 
different cases we need the powers of retention, 
of suggestion and of imagination in very differ- 
ent degrees. In some cases we require to re- 
member a thing only a few moments, or a few 
minutes ; in other cases a few hours or days ; in 



174 Oiq- THE KliTOWIKG FACULTIES 

yet other cases a few weeks or months : it is an 
iniinitesimally small part of all our mental impres- 
sions which can be profitably remembered for 
years. Memory may be too retentive, and facil- 
ity of forgetting and of driving out one train of 
ideas by a new train is almost as essential to a 
well-trained intellect as facility of retention. 

' ' Take the case of a barrister in full practice, 
who deals with several cases in a day. His busi- 
ness is to acquire as rapidly as possible the facts 
of the case immediately before him. With the 
powers of representation of a well-trained mind, 
he holds these facts steadily before him, compar- 
ing them with each other, discovering their re- 
lations, applying to them the principles and rules 
of law more deeply graven on his memory, or 
brino-iiio- them into connection with a few of the 
more prominent facts of previous cases which he 
happens to remember. For the details of laws 
and precedents he trusts to his text writers, the 
statute book, and his law library. Even before 
the case is finished his mind has probably sifted 
out the facts and rejected the unimportant ones 
by the law of obliviscence. One case done with, 
he takes up a wholly new series of facts, and so 
from day to day, and from month to month, 
the matter before him is constantly changing. 
The same remarks are even more true of a busy 
and able administrator like Mr. Cross. The 
points which come before him are infinite in va- 
riety. The facts of each case are rapidly brought 
to his notice by subordinates, by correspondence, 
by debates in the House, by deputations and in- 



OF THE MIKD. 175 

terviews, or by newspaper reports. Applying 
well-trained powers of judgment to the matter in 
Land, lie makes a rapid decision and passes to the 
next piece of business. It would be fatal to Mr. 
Cross if he were to allow things to sink deep into 
his mind and stay there. There would be no 
difficulty in showing that in like manner, but in 
varying degrees, the engineer, the physician, the 
merchant, even the tradesman or the inteUigent 
artisan, deal every day with various combina- 
tions of facts which cannot all be stored up in 
the cerebral framework, and certainly need not 
be so. 

'' The bearing of these considerations upon 
the subject of examinations ought to be very 
evident. For what is ' cram ' but the rapid ac- 
quisition of a series of facts, the vigorous getting 
up of a case, in order to exhibit well-trained 
powers of comprehension, of judgment, before an 
examiner ? The practised barrister ' crams ' up. 
his * brief ' (so called because, as some suppose, 
made brief for the purpose) and stands an ex- 
amination in it before a judge and jur}^ The 
candidate is not so hurried ; he spends months 
or it may be two or three years in getting up 
his differential calculus or his inorganic chemis- 
try. It is quite likely that when the ordeal is 
passed, and the favourable verdict delivered, he 
will dismiss the equations and the salts and com- 
pounds from his mind as rapidly as possible ; but 
it does not follow that the useful effect of his 
training vanishes at the same time. If so, it fol- 
lows that almost all the most able and successful 



176 OlSr THE KNOWING FACULTIES 

men of the present day tlirew away tlieir pains at 
school and college. I suppose tliat no one ever 
heard of a differential equation solving a nice point 
of law, nor is it common to hear Sophocles and 
Tacitus quoted by a leading counsel. Yet it can 
hardly be denied that our greatest barristers and 
judges were trained in the mathematical sciences, 
or if not, that their teachers thought the classics 
a better training ground. If things taught at 
school and college are to stay in the mind to 
serve us in the business of life, then almost all 
the higher education yet given in this kingdom 
has missed its mark. I come to the conclusion, 
then, that well-ordered education is a severe 
system of well-sustained ' cram. ' . . . We 
cannot consider it the work of teachers to make 
philosophers and scholars and geniuses of various 
sorts : these, like poets, are born not made. 
Nor, as I have shown, is it the business of the 
educator to impress indelibly upon the mind the 
useful knowledge which is to guide the pupil 
through life. This would be ' cram ' indeed. It 
is the purpose of education so to exercise the 
faculties of mind that the infinitely various expe- 
rience of after-life may be observed and reasoned 
upon to the best effect. AVhat is popularly con- 
demned as ' cram ' is often the best devised and 
best conducted system of training towards this 
all-important end." (Jevons, ' (7ra?7i, ' art. in 
Mhid, pp. 193-207, No. VI., April, 1877.) 

173. " The act of knowing is that activity of 
the mind by means of which it consciously repro- 
duces in itself what actually exists. The act of 



OF THE MIXD. 177 

knowing is partly immediate or outer and inner 
perception, partly mediate or thinking. The 
regulative laws (injunctions, prescriptions) are 
those universal conditions to which the activity 
of knowledge must conform in order to attain to 
the end and aim of knowledge." (Ueberweg, 
Hist. Log. Doct., p. 1, ed. 1871.) 

174. "Knowledge, in the wider sense in 
which we here use the word, comprehends both 
cognition, which rests on perception (and on the 
evidence transmitting perceptions of which we 
are ignorant), and also knowledge in the stricter 
sense, which is attained by thinking. 

175. " The act of knowing, in so far as it is 
the copying in the human consciousness of the 
essence of the thin^, is an after-thinkino- of the 
thouo'hts which the divine creative thinkino- has 
built into things. In action the preceding 
thought determines what actually exists, but in 
knowing the actual existence, in itself conform- 
able to reason, determines the human thought." 
(Ibid., p. 2.) 

176. "1. The objective existence to he 
known consists not merely of natural objects, 
hut also (as in history, etc. ) of mental contents. 
2. The mirroring in consciousness, although re- 
production, cannot be accomplished without a 
peculiar activity of the mind. 3. The whole ac- 
tivity of the mind is not exhausted in knowledge. 
There is besides the creative power of the phan- 
tasy, reforming and refining what is given in the 
conception, and ethical action." (Ibid,, pp. 
2-3.) 



178 01^ THE kkowi:n"g faculties 

177. ''Knowledge of fact is knowledge by 
onlook ; knowledge inferred is knowledge of one 
thing through means of another : knowledge of 
first principles is knowledge by insight into truth 
higher than fact. ' ' (Calderwood, Hand Book, 
Moral Phil, p. 3.9, ed. 1879.) 

178. In giving the difference between 
Thought, properly so called, and other phenom- 
ena of the mind, I cannot do better than to quote 
the following : " Every state of consciousness 
necessarily implies two elements at least : a con- 
scious subject, and an object of which he is con- 
scious. In every exercise, for example, of the 
senses, we may distinguish the object seen, heard, 
smelt, touched, tasted, from the subject seeing, 
hearing, smelling, touching, tasting. In every 
emotion of pleasure or of pain, there is a certain 
affection, agreeable or disagreeable, existing 
within me, and of this affection I am conscious. 
In every act of volition, there takes place a certain 
exercise of my will, and I am conscious that it 
takes place. . . . But to constitute an act 
of Thought, more is required than the immedi- 
ate relation of subject to object in consciousness. 
Every one of the above states might exist in a 
mind totally incapable of thought. Let us sup- 
pose, for example, a being, in whose mind every 
successive state of consciousness was forgotten 
as soon as it had taken place. Every individual 
object might be presented to him precisely as it 
is to us. Animals, men, trees, and stones, might 
be successively placed before his eyes ; pleasure, 
and pain, and anger, and fear, might alternate 



OF THE MIKD. 179 

witliin liim ; but, as eacli departed, lie would re- 
tain no knowledge that it liad ever existed, and 
consequently no power of comparison with simi- 
lar or dissimilar objects of an earlier or later con- 
sciousness. He would have no knowledge of 
such objects as referred to separate notions ; 
he could not say, this which I see is a man, or a 
horse ; this which I feel is fear, or anger. He 
would be deficient in the distinctive feature of 
Thought, the concept or general notion resulting 
from the comparison of objects. Hence arises 
the important distinction between Intuitions, in 
which the object is immediately related to the 
conscious mind, and Thoughts, in which the ob- 
ject is mediately related through a concept 
gained by comparison. . . . By Intuition 
is meant to include all the products of the per- 
ceptive (external and internal) and imaginative 
faculties ; every act of consciousness, in short, 
of which the immediate object is an individual, 
thing, act, or state of mind, presented under the 
condition of distinct existence in space or time. 
It is necessary to distinguish between the act of 
thought and its product — the former is desig- 
nated by the term conception, the product by 
concept. . . . Intuition contains two ele- 
ments only, the subject and the object standing 
in present relation to each other. Thought con- 
tains three elements, the thinking subject, the 
object about which he thinks, and the concept 
mediating between the two. Thus even the ex- 
ercise of the senses upon present objects, in the 
manner in which it is ordinarily performed by a 



180 ON" THE KNOWING FACULTIES 

man of mature faculties, does not consist of mere 
intuition, but is accompanied by an act of 
thought. In mere intuition, all that is simulta- 
neously presented to the sense appears as one 
whole ; but mere intuition does not distinguish 
its several parts from each other under this or 
that notion. I may see at once, in a single pano- 
rama, a ship upon the sea, an island lying be- 
hind it, and the sky above it. To mere intui- 
tion this is presented only in confusion, as a sin- 
gle object. To distinguish its constituent por- 
tions, as sea and land, ship and sky, requires a 
comparison and classification of them relatively 
to so many separate concepts existing in the 
mind ; and such classification is an act of 
Thought. 

In every act of Consciousness the ultimate ob- 
ject is an individual. But in intuition this ob- 
ject is presented to the mind directly, and does 
not imply the existence, past or present, of any- 
thing but itself and the mind to which it is pre- 
sented. In thought, on the other hand, the in- 
dividual is represented by means of a concept, 
which contains certain attributes applicable to 
other individuals of the same kind. This im- 
plies that there have been presented to the mind 
prior objects of intuition, originating the con- 
cept or general notion to which subsequent objects 
are referred. Hence arises another important 
distinction. All intuition is direct and presen- 
tative ; all thought is indirect and representative. 
. By representation are here included the 
concept, which is representative of many indi- 



OF THE MIKD. 181 

vi duals, and the image, which is representative 
of one. . . . Perception is employed to de- 
note all those states of Consciousness which are 
presentative only, not representative. It will 
thus include all intuitions except those of Imagi- 
nation. . . . The office of the faculty of 
Imagination, whose office is the production of 
images representative of the several phenomena 
of Perception, internal as well as external. . . . 
Imagination, regarded as a product, may be de- 
fined, the consciousness of an image in the mind 
resembling and representing an object of intui- 
tion. It is thus at the same time presentative 
and representative. It is presentative of the 
image which has its own distinct existence in 
consciousness, irrespective of its relation to the 
object which it is supposed to represent. It is 
representative of the object which that image re- 
sembles ; and such resemblance is only possible 
on the condition that the image be, like the ob- 
ject, individual. . . . The distinguishing 
feature of a concept is, that it cannot in itself 
be depicted to sense or imagination. It is 
not the sensible image of one object, but an in- 
telligible relation between many. A second im- 
portant characteristic of all concepts is, that they 
require to be fixed in a representative sign, 
which is language." (Mansel, Prolegomena 
Locjim, pp. 20-6, ed. 1860.) 

179. " In a psychological point of view, to 
enumerate separate mental faculties and opera- 
tions, as giving rise to the various products of 
thought, is, to say the least, to encumber the 



183 OlS" THE KI^OWIKG FACULTIES 

science with unnecessary and perplexing distinc- 
tions. It will be sutticient to refer them to the 
single faculty of thought or reflection, the oper- 
ation of which is, in all cases, comparison. The 
unit of thought is always a judgment, based on a 
comparison of objects ; and the several operations 
of thought are, in ultimate analysis, nothing 
more than judgments derived from different 
data. In order to exhibit this in special in- 
stances, it will be convenient to adopt provision- 
ally the logical classification, and to examine the 
phenomena of thought under the several heads 
of Conception, Judgment, and Reasoning." 
(Mansel, Metaphysics, pp. 176-7, ed. 1871, New 
York.) 

180. " In a psychological point of view, to 
enumerate separate mental faculties, as giving 
rise to the various products of thought, is, to 
say the least, to encumber the science with un- 
necessary and perplexing distinctions. It will 
be sufficient to refer them to the single faculty 
of Thought, the operation of which is in all 
cases Comparison (see Hamilton, Led. on Meta- 
physics, Led. xxxiv.). But the faculty of 
Thought, though uniform in its own nature and 
in the manner of its operation, may yet give 
rise to different products, according to the di- 
versity of the materials upon which it operates ; 
and this difference forms the basis of the classi- 
fication usually adopted in Logic. Extending 
the terms Apprehension and Judgment beyond 
the region of Thought proper (into Psychology), 
it may be laid down, as a general canon of Psy- 



OF THE MIKD. 183 

chology, that the unit of consciousness is a 
judgment; in other words, that every act of 
consciousness, intuitive or discursive, is com- 
prised in a conviction of the presence of its ob- 
ject, either internally in the mind or externally 
in space. The result of every such act must 
thus be generally stated in the proposition, 
" This is here." Consequently, at least with 
reference to the primary and spontaneous, as 
distinguished from the secondary and reflex acts 
of consciousness, it is more correct to describe 
Apprehension as the analysis of Judgments, than 
Judgment as the synthesis of Apprehensions. In 
a psychological point of view, therefore, it is in- 
correct to describe Simple Apprehension as the 
first operation of the mind. In one sense, in- 
deed, the relation of prior and posterior is al- 
together out of place : Chronologically, inas- 
much as every Apprehension is simultaneous 
with a Judgment, and every Judgment with 
an Apprehension ; and logically, inasmuch as 
Judgment cannot exist without Apprehension, 
nor Apprehension without Judgment. In an- 
other sense, however, we may properly say that 
Judgment is prior to Apprehension ; meaning 
that the subject and the object are first given 
in their mutual relation to each other, before 
either of them can itself become a separate 
object of attention. But when a correspond- 
ing division is adopted of the operation of 
Thought, properly so called, the same order of 
priority cannot be observed. Every operation 
of thought is a judgment, in the psychological 



184 ON" THE KN"OWIN^G FACULTIES 

sense of the term ; hut the psychological judg- 
ment must not be confounded with the logical. 
Tlie former is the judgment of a relation between 
the conscious subject and the immediate object 
of consciousness ; the latter is the judgment of 
a relation which two objects of thought bear to 
each other. The former cannot be distinguished 
as true or false, inasmuch as the object is there- 
by only judged to be present at the moment 
when we are conscious of it as affecting us in a 
certain manner ; and this consciousness is nec- 
essarily true. The latter is true or false accord- 
ing as the relations thought as existing between 
certain concepts are actually found in the ob- 
jects represented by those concepts or not. 
The logical judgment necessarily contains two 
concepts (products of thought), and hence must 
be regarded as logically and chronologically pos- 
terior to the conception (act of thought), which 
requires one only. The psychological judgment 
is coeval with the first act of consciousness, and 
is implied in every mental process, whether of 
intuition or of thought. It cannot, therefore, be 
called prior or posterior to any other mental op- 
eration, for there is no mental operation in 
which it does not take place ; but the judgments 
of intuition are logically and chronologically 
prior to the judgments of thought. Conception 
is a psychological judgment, but not a logical 
one, and is properly ranked as the first operation 
of Thought, inasmuch as it is the simplest. . . . 
Conceiving has been already explained as 
the individualizing of certain attributes compre- 



OF THE MIKD. 185 

tended in a general notion and expressed in a gen- 
eral term ; the representation, namely, of such 
attributes as coexisting in a possible object of 
intuition. Language is, . . . in its earliest 
operations, a sign, not of concepts, but of intu- 
itions. Its earliest terms are employed as the 
proper names of individual objects. Conception 
does not take place till after we have learned to give 
the same name to various individuals presented 
to us with certain differences of attributes, and 
hence we associate it with a portion only, not 
with the whole, of what is presented in each. 
This may be distinguished as Abstraction, a 
spontaneous, though not always a voluntary act, 
the concentration of the mind on certain portions 
only of a given object in relation to its name. 
This must not be treated . . as a conscious process 
of thought, being only a preliminary condition 
to thinking, taking place in the majority of 
cases unconsciously, during the gradual acquisi- 
tion of speech. Our names thus gradually ac- 
quire a signification, being transformed from 
proper names to appellatives. Finally, the act 
of conception consists in contemplating the at- 
tributes thus combined in the signification of a 
name as coexisting, along with individual fea- 
tures, in a possible object of intuition, and hence, 
apart from the individual features, as indiffer- 
ently representing all such objects. This repre- 
sentative collection of attributes, combined by 
means of a sign, is a Concept. . . . As in 
Conception a single general notion is considered 
in its relation to a possible object of intuition, 



186 0^ THE KNOWIJ^G FACULTIES 

SO in Judgment' two such notions are considered 
as related to a common object. When I assert 
that A is B, I do not mean that the attributes 
constituting the concept A are identical with 
those constituting the concept B, — for this is 
only true in identical judgments, — but that the 
object in which the one set of attributes is found 
is the same as that in which the other set is found. 
. The common language and common 
thought of mankind assume, whether they ex- 
plam it or not, that a certain smell and color 
and form, which are distinct attributes, are in 
some way related, as parts or qualities, to some 
one thing which we call a rose ; and that, when 
I assert that the rose is fragrant, I imply that 
the thing which affects in a certain way my 
power of sight is in some manner identical (Iden- 
tity) with that which affects in a certain way my 
power of smell. . . . Reasoning is the most 
complex of the three operations, as in it two 
concepts are determined to be in a certain man- 
ner related to each other, through the medium 
of their mutual relations to a third concept. 
This operation is therefore treated last in order. 
The several relations asserted in the premises 
and deduced in the conclusion, are of the same 
nature as those implied in Judgment. 
It will be sufficient to attempt . . a definition of 
the products of the several acts of Thought, the 
Concept, the Judgment, and the Syllogism, the 
legitimate objects of Formal Logic. 1. A Con- 
cept is a collection of attributes, united by a 
sign, and representing a possible object of intui- 



OF THE MIKD. 187 

tion. 2. A Judgment is a combination of two 
concepts, related to one or more Common ob- 
jects of possible intuition. 3. A Syllogism is a 
combination of two judgments, necessitating a 
third judgment as tlie consequence of tbeir mu- 
tual relation." (Mansel, Prolegomena Logica, 
P2>. 62-9, ed. 1860.) 

181. " The mental powers employed in the 
acquisition of knowledge are probably three in 
number. They are substantially as Professor 
Bain has stated them (^Senses and Intellect, 2d 
ed., pp. 5, 325, etc.): — 1. The Power of Discrim- 
ination ; 2. The Power of Detecting Identity ; 
3. The Power of Retention. We exert the first 
power in every act of perception. 'Hardly can 
we have a sensation or feeling unless we discrim- 
inate it from something else which preceded. 
Consciousness would almost seem to consist in 
the break between one state of mind and the 
next, just as an induced current of electricity 
arises from the beginning or the ending of the 
primary current. We are always engaged in dis- 
crimination ; and the rudiment of thought 
which exists in the lower animals probably con- 
sists in their power of feeling difference and be- 
ing agitated by it. Yet had we the power of 
discrimination only. Science could not be created. 
To know that one feeling differs from another 
gives purely negative information. It cannot 
teach us what will happen. In such a state of 
intellect each sensation Avould stand out distinct 
from every other ; there would be no tie, no 
bridge of affinity between them. We want a 



188 01^ THE KNOWING FACULTIES 

unifying power by wliicli tlie present and the fu- 
ture may be linked to the past ; and tbis seems 
to be accomplished by a different power of mind. 
Lord Bacon has pointed out that different men 
possess in very different degrees the powers of 
discrimination and identification. It may be said 
indeed that discrimination necessarily implies 
the action of the o}>posite process of identifica- 
tion ; and so it doubtless does in negative points. 
But there is a rare property of mind which con- 
sists in penetrating the disguise of variety and 
seizing the common elements of sameness ; and 
it is this property wliich furnishes the true mea- 
sure of intellect. The name of ' intellect ' expresses 
the interlacing of the general and the single, which 
is the peculiar province of mind. (Max Miiller, 
Led. Sci. Lang., Id series, Vol. II., p. 63). 

Plato said of this unifying power, that if 
he met the man who could detect the one in the 
many, he would follow him as a god. ' ' ( Jevons, 
The Princ. of Science, pp. 4-5, eel. 18V7.) 

" LAWS OF IDENTITY AND DIFFERENCE. 

182. '' At the base of all thought and science 
must lie the laws which express the very nature 
and conditions of the discriminating and identi- 
fying powers of mind. These are the so-called 
Fundamental Laws of Thought, usually stated as 
follows : — 

1. The Law of Identity. Whatever is, is. 

2. The Law of Contradiction. A thing can- 
not both be and not be. 



OF THE MIND. 189 

3. The Law of Duality. A thing must 
either be or not be. 

' ' The first of these statements may perhaps be 
regarded as a description of identity itself, if so 
fundamental a notion can admit of description. 
A thing at any moment is perfectly identical with 
itself, and, if any person were unaware of the 
meaning of the word ' identity,' we could not 
better describe it than by such an example. 

*' The second law points out that contradictory 
attributes can never be joined together. The 
same object may vary in its different parts ; here 
it may be black, and there white ; at one time it 
may be hard and at another time soft ; but at 
the same time and place an attribute cannot be 
both present and absent. Aristotle truly de- 
scribed this law as the first of all axioms — one 
of which we need not seek for any demonstra- 
tion. All truths cannot be proved, otherwise 
there would be an endless chain of demonstra- 
tion ; and it is in self-evident truths like this 
that we find the simplest foundations. 

' * The third of these laws completes the other 
two. It asserts that at every step there are two 
possible alternatives — presence or absence, affir- 
mation or negation. Hence I propose to name 
this law the Law of Duality, for it gives to all 
the formulae of reasoning a. dual character. It 
asserts also that between presence and absence, 
existence and non-existence, affirmation and ne- 
gation, there is no third alternative. As Aris- 
totle said, there can be no mean between oppo- 



190 OK THE KN-QWIKG FACULTIES 

site assertions : we must either affirm or deny." 
[Ih'uL, pp. 5-6.) 

183. " The primitive and essential gradation 
of thought we have indicated to be the Judg- 
ment. In accordance with what has been said, 
a Judgment may be defined to be a recogni- 
tion of the identity or non-identity between 
any two objects presented to the Faculty of 
Thought. As expressed in words, a Judgment 
is called a Proposition, or in grammatical no- 
menclature, a Sentence. 

'' Besides the Judgment, there are two other 
products of thought, both derivatives from the 
Judgment. The one is the Concept, which is 
derived from several Judgments by an act of 
Conceiving — taking together, in other words, 
by an act of synthesis. The other is the Bea- 
soning, which is derived from one or more Judg- 
ments by an act of analysis or separation. As 
all thought is essentially a movement in Quan- 
tity, and as variations in Quantity can be affected 
only m the one or the other of these two direc- 
tions, synthesis and analysis, the Concept and 
the Reasoning are the only conceivable deriva- 
tives from a Judgment, except such as consist 
only in variations of form, that do not affect 
the identity of the thought. 

' ' In explication of this definition of a Judg- 
ment, it will be necessary simply to recall what 
has been already said in the exposition of the 
general nature of thought. As we have seen, 
a judgment necessarily supposes two objects ; 



OF THE MII^D. 191 

and its essential characteristic, as an act of In- 
telligence, consists in tliis : that it is a cognition 
of this particular relation of identity- or non- 
identity between the two objects. These two 
objects of a judgment are given to it by some 
other faculty of the Intelligence, as of Percep- 
tion, Intuition, Memory, or by the Discursive 
Faculty itself, in some previous exercise. It 
may be some object of Perception, as Bucephalus. 
As thus given by the Perceptive Faculty, the 
cognition is of an object by itself, without rela- 
tion either to other objects or to the parts of 
the object itself. Color is not in the percep- 
tion itself distinguished from figure ; neither 
color nor figure from the position or the time 
in Avhich it is perceived ; and neither of 
these from the useful qualities of the object. 
All the perceptible qnali ies are given together 
without distinction iu the presentation itself 
of the object. But when thus given, the 
mind at once, and by a kind of necessity of its 
being as essentially active and reflective, exerts 
its activity on it, first, by apprehending it as 
a part of a multiplicity of objects around, 
to each of which it stands in relation, and also, 
as a whole, containing parts in itself. This is 
the primitive and conditional gradation in all 
thought — the apprehension of an object as a part 
or as a whole — in other words, in the relation of 
Quantity. Simultaneously with this, it appre- 
hends some other object of thought given to it 
by Perception, or by some other Faculty of the 
Intelligence, or in some previous exercise of the 



192 Oiq* THE K1T0WIN"G FACULTIES 

Judgment, and thus comes to view the two ob- 
jects thus given in relation to each other, as the 
same or not the same. Its act then becomes 
complete ; and a perfected product of thought, 
a Judgment, is the result. Thus the second ob- 
ject may be given in the Perception itself, as 
black, or four-footed, and the Judgment recog- 
nizes this color or this form as belonging to 
Bucephalus — that is, as identical with one of the 
parts or characters that make up the whole per- 
ception. Or the second object may be given by 
the Regulative Faculty, or Faculty of Intuition, 
as of Being, of Space, of Time, or other idea of 
the proper Reason ; and then the Judgment iden- 
tifies Bucephalus with Existence, with some part 
of Space, of Time ; or in other words, affirms 
Bucephalus to be, to be in such a place, at 
such a time, and the like. The second object 
of thought may, in like manner, be given to the 
Judging Faculty by the Memory. We may 
identify Bucephalus as now perceived with the 
Bucephalus perceived yesterday ; with the black 
color, the four-footed figure, before perceived in 
some other object. 

" The essential nature of a Judg-ment, thus, 
is seen to be an identification of one object 
with another, either totally or partially — in some 
one or in all respects. It is accordingly a rela- 
tive cognition ; and m the relation which it in- 
volves are necessarily contained three elements : 
1. The object of thought identified with some 
other. 2. The object with which it is identi- 
fied, either in whole or in part. And, 3. The 



OF THE MIKD. 193 

mental act which identifies. The first two con- 
stitute the matter of thought, the datum ; tlie 
last is the Thought itself, the identifying cogni- 
tion — the Judgment. 

" To the several parts, or to different aspects 
of the complex procedure in all Thought as 
thus exemplitied in one of its gradations — the 
Judgment — Psychology has assigned distinctive 
names, which it may not be inexpedient here to 
recall. Inasmuch as the original datum or ob- 
ject of thought is given in an indefinite vagueness 
as one and undivided, and as, in order to be 
cognized in thought, it must be viewed in rela- 
tion to some part, it becomes necessary to loosen 
up, to analyze or separate it as a whole into its 
parts. This part of the process is called Analy- 
sis. 

" The next step is to select the part out of 
the whole for separate apprehension, and to 
draw it away, as it were, to abstract it from the 
other parts. This part of the movement in 
Thought is called Abstraction. The term, how- 
ever, it is proper to add, is applied in various 
ways by different writers or on different occasions, 
but with the same result. Thus it may be ap- 
plied to the mind itself ; so that in Abstraction 
the mind, when confining its view to certain 
parts of an object, is regarded as being abstracted 
or drawn away from tte parts that are to be ex- 
cluded from view ; and this, it may be observed, 
is in strictness the most correct view. But in a 
looser sense the term may be applied to the part 
itself that is selected, and then such part is re- 



194 ON" THE KJ^OWIITG FACULTIES 

garded as being abstracted from the other parts. 
Or, in the third place, it may be applied to 
those other excluded parts themselves, and then 
they are regarded as being abstracted or drawn 
away either from the other parts or from the 
mind's consideration. The result is the same 
in any view% that one part is separated from the 
other parts for exclusive consideration, and it is 
therefore a matter ot indifference, so far as the 
result is concerned, which of these different 
views is entertained. 

** When thus one part is separated from the 
rest for exclusive consideration by the mind, the 
act of mind in which it concentrates its notice 
upon it is called Attention. 

"In the next place, the tw^o objects are 
brought up and viewed face to face with each 
other in order that their identity or non-identity 
may be apprehended. This part of the process 
is called Comparison. 

" Finally, the last part of the complex pro- 
cess, in which the thought is perfected by bring- 
ing together the two objects attended to into one 
relative cognition, is called an act of Synthesis. 

' ' All Thought thus begins with an Analysis, 
it proceeds by Abstraction, Attention, and Com- 
parison, it ends with a Synthesis. And this is 
to be understood in a sense more or less full 
and complete, in modes varying with the nature 
of the particular gradation of all the acts of 
thought, whether in judging, conceiving, or 
reasoning. The two essential elements of thought 
are analysis and synthesis. With one it neces- 



OF THE MIKD. 195 

sarily begins, with the other it necessarily ends. 
For its very function is to lead to truth, to a 
unity in the intelligence, which supposes an un- 
distinguished manifold as its condition, and a 
gathering into a unity as its result. The other 
parts of the complex process, abstraction, atten- 
tion, and comparison, are the means by which 
the mind passes from the multiform given in the 
analysis to the unity in the synthesis. 

" Of the two objects of thought identified in 
a Judgment, one is necessarily viewed as the 
primitive which is to be identified with the other, 
or is detennined by it. This so viewed primi- 
tive or determined object is called the Subject; 
which may be defined to be that of which we 
judge. The other, viewed as the determining 
element, is called the Predicate, which may be 
defined to be that which is judged of the subject. 
The Subject and the Predicate make up the mat- 
ter of thought or the datum to thought. They 
are called the Terms of a Proposition (termini). 
The act of thought itself which recognizes the 
identity between the two terms is called the 
Copula, which may be defined to be the identifi- 
cation of two objects of thought. It was called 
by Aristotle, in reference to the two terms, an 
Interval." (Day, Ele. of Logic, pp. 31-5, ed. 
1868.) 

184. " The Second gradation of Thought is 
the Concept. It is derived from the primitive 
product, the Judgment, by an act of synthesis 
or composition. It accordingly presupposes two 
or more Judgments, and, if a valid product of 



196 OK THE KKOWIKG FACULTIES 

Thought, can always be resolved back into them. 
It can, in fact, be verified only by being thus re- 
ferred back to the Judgments from which it is 
derived. It is formed either by the synthesis of 
the Subjects of two or more Judgments, or by 
a synthesis of their Predicates — an alternative 
which gives rise to the two fundamental classes 
of Concepts. It may conduce to clearness to 
exemplify the process of forming the Concept in 
these two ways separately. 

*' First, then, if we synthesize the subjects, 
the procedure will be as follows : The Judg- 
ments, out of which the Concept is to be formed, 
we will assume to be — Socrates is rational; 
Cicero is rational ; James is rational. By 
uniting the subjects, we have Socrates and Cicero 
and James, and marking the union by a single 
term which sha') embrace them all in one, we 
will say, man, we have the union signalized in 
language. This union of the differing subjects 
of several propositions having a common predi- 
cate is called a Concept ; in this case a Concept 
in Extensive Quantity. The formula for the 
formation of all Concepts of this class is, accord- 
ingly : The Judgments, B is A, C is A, give the 
Concept (B-l-C), or when signalized in language 
by one term, the Concept D ; or in brief : The 
Judgments B is A, C is A, give B + C = the Con- 
cept B. 

"The procedure in forming Concepts of the 
other class is analogous. Here the Subject re- 
mains the same, and the Concept arises from the 
synthesis of the Predicates which differ. Thus, 



OF THE MIIS'D. 197 

the Predicates in the Judgments, Socrates is ra- 
tional, Socrates is animal, being united, we have 
rational and animal, or signalizing the union 
by a single term, we have the Concept, Man. 
The term Man here, it will be observed, means 
a complement of attributes, as rational, animal, 
not, as before, of subjects, as Socrates, &c. 
This is a concept in Comprehensive Quantity ; 
the formula of which is : The Judgments A is 
B, A is C, give, by synthesis of the differing 
Predicates, the aggregate (B + C), which signal- 
ized as one in Language is expressed by D. Or 
the Judgments A is B, A is C, give Concept 
(B + C)=D. 

" A Concept may be defined, accordingly, to 
be a product of Thought, resulting from the 
synthesis of the Subjects or of the Predicates in 
several Judgments. 

" The common Subject in a Predicate-Con- 
cept, or the common Predicate in a Subject- 
Concept, on which the Concept is formed, is 
called its Base. 

" The name, Concept, is derived from the 
Latin word Conceptum, meaning somethings 
taken with another. The corresponding word 
used to denote the act of forming a Concept is 
Conception, which is also in common discourse 
often used to denote the product. It is used, 
in fact, like other words of this kind, in the three- 
fold import of faculty, act, and product. 

" The Law of Identity, or as, in its fuller 
expression, it may be denominated, the Law of 
the Same and Different, it will have been seen, 



198 Oiq" THE KNOWIKG FACULTIES 

presides over tliis product of Thought, as over 
the Judgment. No vaUd Concept can be formed, 
unless from Judgments which have either iden- 
tical subjects or identical predicates. The Con- 
cept arises from the Synthesis of the different 
under the same ; of different subjects having 
the same predicate, or of different predicates 
having the same subject. In other words, in the 
Base is to be found the identifying principle 
governing in the Concept. 

'' It will have been observed, moreover, from 
the mode of its formation that a Concept is es- 
sentially a relative cognition. It is not only 
the result of a synthesis, not only the aggregate 
of a plurality of Judgments, and accordingly of 
relative cognitions, but the cognitions that are 
brought together in this synthesis sustain a de- 
termined and peculiar relation to one another. 
If the Concepts be formed from the subjects of 
the Judgments, those Judgments must have a 
common — the same predicate ; if from the pred- 
icates, the Judgments must have the same sub- 
ject. Concepts are thus from their very nature 
relative cognitions, and the principle of relation 
is in the sameness of the term of the Judgment 
which is not synthesized into the Concept — in 
its Base. 

' ' Concepts, however, differ from Judgments, 
as relative cognitions, in this respect : that in 
the Judgment the relation is explicit, while in 
the Concept it is only implied. Thus' in the 
Judgment, Man is a rational animal, the rela- 
tion is articulately declared ; but in the Concept, 



OE THE MIKD. 199 

Man, the reb.tion to the other term of the Judg- 
ment from which it is derived, although real, is 
not expressed, but only implied. The Base of 
the Concept, although real, is not expressed. 

" Still further, a Concept is essentially a one- 
sided cognition. It is formed from but one side 
of a Judgment, from the Subject or from the 
Predicate. It may be regarded, indeed, as an 
aggregate of Judgments, that is, a synthesized 
or composite Judgment, with the single term — 
the Base, and the Copula dropped. 

" A Concept, however, always implies the 
Judgments from which it is derived ; it implies 
the other term, which has been dropped, but 
which is the indispensable condition of its being 
formed, and is, therefore, appropriately denomi- 
nated the Base of the Concept ; and also implies 
that this Base has been identified with each of 
the terms which compose the Concept. 
It will occur to the reflecting mind, on this ex- 
position of the mode in which Concepts are 
formed, that they are mere products of Thought, 
aggregates of Subjects, or aggregates of Predi- 
cates, and do not imply necessarily any exactly 
corresponding aggregates in the reality of things. 
How many individual subjects of Judgments 
shall be combined, or how many predicates, are 
questions that will be determined by such con- 
siderations as those of extent of observation, 
practicability of aggregation, convenience of use, 
the needs of occasion, and the like. The ex- 
tent of the aggregation, therefore, varies indefi- 
nitely with the occasions of Thought ; and it is 



200 Oiq" THE Kl^OWIKG FACULTIES 

not to be supposed that the constitution of things 
around us fluctuates precisely with the fluctua- 
tions of Thought. As the mathematical analyst, 
in the progress of his demonstration, finds it con- 
venient to substitute single letters or symbols to 
denote a number of quantities in some respect 
of like character, so Thought, for its own mani- 
fold conveniences, often aggregates like elements 
and signahzes them by single words." (Day, 
FAements of Logic ^ ed. 1868, pp. 62-66.) 

185. " The Third gradation of Thought is 
the lieasoning* Like the Concept, it is de- 
rived from the Judgment. It differs from the 
Concept in its form, as, unlike that, it retains the 
full forms of the Judgment, and accordingly, also, 
to a certain extent, it differs from it in the mode 
of its derivation. It differs from the Judgment 
proper in this respect, that it is a derivatioa 
from a Judgment — a traced movement of 
Thought, supperadded to that which constituter. 
the Judgment. It is not the derived Judgment, 
not the mere terminus, the point at the end of 
the line over which the Thought has moved, but 
the line itself as traced in the movement of the 
Thought. When viewed as a resultant product 
of Thought, therefore, it must be regarded as 
the track of Thought left marked by the move- 
ment, not the mere attained object or goal of the 
movement, which is nothing more than a Judg- 
ment. We are carefully to distinguish, there- 
fore, a Reasoning from the Conclusion — from the 
Judgment which is attained by the reasoning. 

' ' A Beasoning, thus, is a derivation of a Judg- 



OF THE MIKD. 201 

ment from another Judgment or Judgments. 
* Keasoning is a modification from the 
French raisonner (and this is a derivation from 
the Latin ratio), and corresponds to ratiociatio, 
which has indeed been immediately transferred 
into our language under the form of ratiocina- 
tion. Ratiocination denotes properly the pro- 
cess, but improperly, also, the product of reason- 
ing ; Ratiocinium marks exclusively the product. 
The original meaning of ratio was computa- 
tion, and from the calculation of numbers it was 
transferred to the process of mediate comparison 
in general. Discourse (discursus, diavoia) in- 
dicates the operation of comparison, the running 
backward and forward between the characters or 
notes of objects (discurrere inter notas, diavo- 
eiaSai). The terms discourse and discursus, 
didvoia, are, however, often used for the reason- 
ing process, strictly considered, and discursive is 
even applied to denote mediate, in opposition to 
intuitive, judgment, as is done by Milton. The 
compound term, discourse of reason, unambig- 
uously marks its employment in this sense. Ar- 
gumentation is derived from argumentari, 
which means argumentis uti ; argument again, 
argumentum — what is assumed in order to argue 
something — is properly the middle notion in a 
reasoning — that through which the conclusion is 
established ; and by the Latin Rhetoricians it 
was defined, ' probabile inventum ad faciendam- 
fidem. ' It is often, however, applied as co-exten- 
sive with argumentation. Inference or Illation 
(from infero) indicates the carrying out into the 



202 OK THE Kiq-QWIiq^G FACULTIES 

last proposition what was virtually contained in 
the antecedent judgments. To conclude (con- 
cludere), again, signifies the act of connecting 
and shutting into the last proposition the two 
notions which stood apart in the two first. A 
conclusion (conclusio) is usually taken, in its 
strict or proper signification, to mean the last 
proposition of a reasoning ; it is, sometimes, 
however, used to express the product of the 
whole process. To syllogize means to form syl- 
logisms. Syllogism {(rvXA^oyiffjuos) seems origi- 
nally, like ratio, to have denoted a computa- 
tion — an adding up ; and like the greater part 
of the technical terms of Logic in general, was 
brorrowed by Aristotle from the mathematicians. 
2vXXoyi(T/.ioS may, however, be considered 
as expressing only what the composition of the 
word denotes — a collecting together ; for aiA- 
XoyiL,8()dai comes from (JvXXeysiVy, which 
signifies to collect. Finally, in Latin, a syllog- 
ism is called coUectio, and to reason, coUigere. 
This refers to the act of collecting, in the conclu- 
sion, the two notions scattered in the premises.' 
" A Reasoning is composed of two parts — the 
original Judgment or Judgments which are the 
original datum in the process, and the move- 
ment of the Thought in the process. As the 
datum is regarded as logically determining and 
preceding, it is called the Antecedent, and the 
other part, regarded as logically determined, or 
following, is called the Conseq^uent. Its proper 
sign is therefore. These are the parts of a 
Reasoning regarded as an Integrate Whole. 



OF THE MIKD. 203 

'' The antecedent in a Reasoning may consist 
of a single Judgment, or of a plurality of Judg- 
ments. If it consist of but one Judgment, the 
Reasoning is called an Immediate Eeasoning ; 
as, Man is a rational animal ; therefore, Man is 
rational. If the antecedent consists of more 
than one Judgment, the Reasoning is called a 
Mediate Reasoning, or, more technically, a Syl- 
logism." (Bay, ' ^^lements of Logic, ' ' ed. 1868, 
pp. 91-94.) 

186. '' Reason, on the other hand, has no 
relation to the body, except as the soul's lodging 
and instrument ; it belongs to the soul, purely 
and abidingly, and may be exercised without 
giving the slightest external token. Instead of 
framing bodily organs, ... it spans the 
sciences, sails deliciously through the heavenly 
realms of poetic analogy, penetrates the signifi- 
cance of things, and looks into the very mind of 
God himself. ' ' (Grindon, Life, p. 365, third ed. , 
London.) 

187. " Thinking, as Plato has observed, is 
but the conversation of the soul with herself ; 
and the instrument employed is the echo of that 
which forms the medium of communication with 
others. To this it may be added that the no- 
tion, as represented in language, is but the sub- 
stitute for the notion embodied in intuition, and 
derives all the conditions of its validity from the 
possibility of the latter ; for language, though 
indispensable as an instrument of thought, lends 
itself with equal facility to every combination, 
and thus furnishes no criterion by which we can 



204 OK THE KATUEE OF 

judge between sense and nonsense — between tbe 
conceivable and the inconceivable." (Mansel, 
Metaphysics, pp. 1671-68, ed. 1871.) 

(b) on the nature of subject-matter. 

188. In addition to a knowledge of mind 
and of knowing, the teacher, engaged in the 
discovery of Methods of Teaching, must dili- 
gently investigate the nature of the subject-mat- 
ter that he is to teach. 

189. By nature of subject-matter is meant 
that subtle, original, and permanent property of 
the subject-matter, at the presence of which tlie 
faculties of the mind are mtuitively incited to 
their specific activities. 

190. Some of this matter lies in the world 
that is external to the mind of man, and is 
called material. 

191. Other matter rests exclusively within 
the ego. The mind creates it both as to its 
matter and form. In the case of material sub- 
ject-matter, the mind determines only the form 
under which it exists as knowledge. In the 
other case, the immaterial, the matter and form 
would never exist as knowledge, or as matter for 
knowledge, were it not for the mind. The in- 
vestigation of this whole subject is too vast to 
attempt to do more, at this time, th?.n touch 
upon two or three subjects, except in the most 
cursory manner. The inquiry is directed towards 
the nature of Object Teaching, a familiar ex- 
pression, and the nature of the subject-matter of 



SUBJECT-MATTEE. 205 

mathematics, one brancli of wliicli, aritlimetic, 
forms so important an element in the lower 
schools. 

192. Object Teaching is that teaching in 
which a knowledge of objects, or object-matter, 
— or where the subject-matters are objects — is 
the real end and purpose of the instruction. Ob- 
ject Teaching regards a knowledge of objects as 
an end — it does not consider anything beyond 
the objects themselves — it is served fully when 
this knowledge of facts is secured — its province 
is with the actual, which exists as individual facts 
— its subject-matter is that which addresses itself 
exclusively to the perceptive and discriminative 
faculties of the mind, as matter to be learned 
for its own sake. The powers of the mind that 
are mainly instrumental in acquisitions by the 
learner, who is taught by Object Teaching, are 
the perceptive, which cognize intuitively and 
immediately ; the discriminative, which outline 
one object from another ; and memory, which 
retains. Whatever is purely distinctive of Object 
Teaching is found within the above limitations. 
It relates to the region of individual facts. 

193. Wherever an abundance of facts is 
wanted as materials for the other faculties of the 
mind to use subsequently in constructing science. 
Object Teaching is the way by which the ne- 
cessities can be met. 

194. But Object Teaching is only possible 
where a knowledge of facts, as such, is to be 
obtained, and where the materials, the matters, 



206 OK THE NATUEE OF 

of knowledge, exist as objects of perception and 
discrimination. 

195. AH tliose ways of teaching where ob- 
jects, as charts, maps, apparatus, pictures, are 
used, by the teacher and pupil, not as ends of 
knowledge unto themselves, but as helps, by 
analogy, to acquiring knowledge of other things 
as ends — all these ways of teaching are not Ob- 
jective, they are Illustrative. 

196. Ideas in the memory are joined together 
by the nexus of their nature, termed the Laws of 
Association. When, by any chance, one idea is 
brought into consciousness from unconsciousness 
— one modification reproduced — the Avhole group 
of ideas, related by sameness of time, space, or 
circumstances, come flitting as flocks through 
consciousness. Connected with this association 
of ideas is the power of imagination, which 
creates new mental beings, and which seizes 
upon analogies. These states or modes of the 
activities make Illustrative Teaching possible. 

197. Illustrations are lights set by the way- 
side in parabolic mirrors, to illuminate obscure 
passages — they are voices which call out a wel- 
come to him who is bewildered in the midst of 
a mazy mass of half-obscured and obscuring 
numbers — they are guides that accompany the 
student to reveal to him on a sudden the secret 
labyrinths through which he may arise into the 
upper levels of light^ — they are the Aladdin Lamp 
and Ring, by whose mystic power their pos- 
sessor may be instantaneously transported into 



SUBJECT-MATTEE. 207 

the palaces of the Beautiful and the True. The 
value of an illustration consists in its brevity, 
its brilliancy, its pointedness, its unexpected and 
unforeseen applicability, and its convincing force 
of plain analogy. 

" Illustration is vivid elucidation ( = to make 
more fully intelligible) by certain specific and 
effective means, as similitudes, comparisons, ap- 
propriate incidents or anecdotes, and the like, 
graphic representations, and even artistic draw- 
ings." (Smith, Syn. Discr.) 

" Analogy is often used familiarly, as if it 
meant mere moral resemblance or similarity. 
Strictly speaking, however, analogy implies a 
third term, or four terms, as follows : — As A is 
to B, so is C ; or as A is to B, so is C to T>. 
Analogy, therefore, is similarity of relations. 
"When we argue from example, we argue from 
the likeness of things ; when from analogy, we 
argue from the likeness of their relations. If I 
argue that, because the seed dies in the earth 
before it springs up anew, therefore it is prob- 
able that the human body will rise again after 
death ; this is, as to the character of the idea, 
a resemblance, as to the argument, an analogy ; 
the principle being that, as the same God is the 
author of a natural and a spiritual world, He 
may be expected to act toward each upon similar 
and common laws. ' ' (Ibid.) 

"Analogy and Induction. — There are two 
requisites iti order to every analogical argument : 
1. That the two or several particulars concerned 
in the argument should be known to agree in 



208 01^ THE NATURE OF 

some one point ; for otherwise they could not be 
referable to any one class, and there would con- 
sequently be no basis to the subsequent inference 
drawn in the conclusion. 2. That the conclusion 
must be modified by a reference to the circum- 
stances of the particular to which we argue. 
For herein consists the essential distinction be- 
tween an analogical and an inductive argu- 
ment." (Fleming, Vocab Phil.) 

198. " I hate set dissertations ; and, above 
all things in the world, 'tis one of the silliest 
things in one of them, to darken your hypothesis 
by placing a number of tall, opake Avords, one 
before another, in a right line, betwixt your 
own and your reader's conception, — when, in all 
likelihood, if you had looked about, you might 
have seen something standing, or hanging up, 
which would have cleared the point at once ; — 
' for what hindrance, hurt, or harm doth the 
laudable desire of knowledge bring to any man, 
if even from a sot, a pot, a fool, a stool, a win- 
ter-mitten, a truckle for a pulley, the lid of a 
goldsmith's crucible, an oil-bottle, an old slipper, 
or a cane-chair V I am this moment sitting 
upon one. Will you give me leave to illustrate 
this affair of wit and judgment, by the two 
knobs on the top of the back of it ? — they are 
fastened on, you see, with two pegs stuck slightly 
into two gimlet-holes, and ^\i\\ place what I have 
to say in so clear a light, as to let you see through 
the drift and meaning of my whole preface, as 
plainly as if every point and particle of it was 
made up of sunbeams. I enter now directly 



SUBJECT-MATTER. 209 

upon the point. Here stands wit, — and there 
stands judgment, close beside it, just Uke the 
two knobs I'm speaking* of, upon the back of 
this self-same chair on which I am sitting. You 
see, they are the highest and most ornamental 
parts of its frame, — as wit and judgment are of 
ours, — and, like them too, indubitably both made 
and fitted to go together, in order, as we may say 
in all such cases of duplicated embellishment, 
to answer one another. Now, for the sake of 
an experiment, and for the clearer illustrating 
this matter, — let us for a moment take off one of 
these two curious ornaments (I care not which) 
from the point or pinnacle of the chair it now 
stands on ; — nay, don't laugh at it, — but did 
you ever see, in the whole course of your lives, 
such a ridiculous business as this has made of it ? 
— Why, 'tis as miserable a sight as a sow with one 
ear ; and there is just as much sense and sym- 
metry in the one as in the other. — Do, — pray, get 
off your seats, only to take a view of it. — Now, 
would any man who valued his character a straw, 
have turned a piece of work out of his hand in such 
a condition ? — Nay, lay your hands upon your 
hearts, and answer this plain question. Whether 
this one single knob, which now stands here like 
a block-head by itself, can serve any purpose 
upon earth, but to put one in mind of the want 
of the other ? — and let me farther ask, in case 
the chair was your own, if you would not in 
your consciences think, rather than be as it is, 
that it would be ten times better without any 
knobs at all ? 



210 O:^ THE NATURE OF 

" Now tliese two knobs, or top-ornaments of 
tlie mind of man, wliich crown the whole entab- 
lature, — being, as I said, wit and judgment, 
which, of all others, as I have proved it, are the 
most needful, — the most prized, — the most cal- 
amitous to be without, and consequently the hard- 
est to come at ; — for all these reasons put togeth- 
er, there is not a mortal among us so destitute of a 
love of good fame or feeding, — or so ignorant of 
what will do him good therein, — who does not 
wish and steadfastly resolve in his own mind, to 
be, or to be thought at least, master of the one 
or the other, and indeed of both of tlicm, if the 
thing seems any way feasible, or likely to be 
brought to pass. ' ' (Sterne, Tristram Shandy, irp. 
88-9, ed. 1844, Philadelphia.) 

199. Illustrative Teaching is seeking some- 
thing that bears a resemblance in form, nature, 
or kind to the point to be learned, or taught, 
presenting it instead of the point, and thus en- 
abling the powers of comparison possessed by 
the pupil to act by inference from the analogy. 
This is a process of extending the meaning of 
words, called sometimes " the process of analo- 
gous or metaphorical extension of the meaning 
of words. This change maj' be said, no doubt, 
to consist in generalization, since there must 
always be a resemblance between the new and 
old applications of the term. But the resem- 
blance is often one of a most distant and obscure 
kind, such as we should call analogy rather than 
identity." (Jevons, El. Lessons in Logic, p. 50, 
ed. 1878.) 



SUBJECT-MATTEK. 211 

200. Example would be something akin to 
analogy, excepting that example may be of the 
kind of thing itself, as well as an example illus- 
trating the case at issue. 

201. Illustrative Teaching is often called, 
unfortunately in conception, Objective Teaching. 
An object can be used for but two possible pur- 
poses in teaching : (1) To be learned, in and 
for itself ; (2) Or to be an aid in learning some- 
thing else. The first is Object Teaching, the 
second is Illustrative Teaching. 

202. The distinction between the province 
of Object Teaching and that of Illustrative 
Teaching has been indistinctly apprehended by 
teachers. This misapprehension has kd to se- 
rious obscurity of conceptions of teaching, for 
the expression Object Teaching has been ap- 
plied without discrimination to all kinds of teach- 
ing where objects were used, whatever their pur- 
pose, whether as objects to be learned, or as ob- 
jects to use in illustrating other points. 

' ' The science which enlightens, and the phys- 
ick that cures, are doubtless very useful : but 
the pretended science that misleads, and the 
physick that kills, are as certainly destructive. 
Teach us, therefore, to distinguish between them. 
It may be replied, as it constantly is, 
the fault is in the physician, and not in the sci- 
ence of medicine, which is otherwise infallible. 
Well, well, be it so : take care, however, the 
physick be never accompanied by the doctor : 
for, as sure as ever they come together, there 
will be an hundred times more to fear from the 



212 ON THE KATUKE OF 

blunders of tLe artist, than to hope for from the 
efficacy of the art." (Rousseau, Emiliiis, Vol. 
L, pp. 45-6.) 

203. It has already been remarked that Ob- 
ject Teaching can be resorted to only with those 
subjects where facts obtained by perception and 
discrimination are desired. There are branches 
to be taught where it is impossible, from the 
nature of the subject-matter, to teach in this 
way. The subject of mathematics is one that 
has grown from a basis of definitions. The axi- 
oms follow definitions, but they are phases of 
conclusive reasoning, and assume things which 
are the creations of definitions. Definitions are 
the bases of mathematic science in its matter. 
Axioms are the bases in its logical processes of 
reasoning. Definitions are things which are prod- 
ucts growing out of relations. Relations are ob- 
jects only as they are products of the activities of 
the faculty of Thought. Hence all mathematical 
subjects are, from their nature, incapable of be- 
ing taught objectively. All lines, mathematical 
blocks, charts, astronomical apparatus, and cal- 
culating machines, are but objects which illus- 
trate mathematical truths, its definitions, and 
results, as intellectual products — they are not the 
things which are learned in themselves. What 
are called Applied Mathematics are only hypo- 
thetical illustrations of mental creations. It is 
also true that this science is one " in whose reas- 
onings both matter and form can be furnished 
by the mind itself," and not one where " the 
form alone is from the mind, the matter being 



SUBJECT-MATTEE. 213 

derived from experience." (Mansel, Prol. Log, 
p. 93, ed. 1860.) 

204. " Abstract terms are strongly distin- 
guished from general terms by possessing only 
one kind of meaning ; for as they denote quali- 
ties there is nothing which they cannot in addi- 
tion imply. The adjective ' red ' is the name 
of red objects, but it implies the possession by 
them of the quality redness ; but this latter 
term has one single meaning — the quality alone. 
Thus it arises that abstract terms are incapable 
of plurality." (Jevons, Prin. Science, p. 27, ed. 
1877.) . . . " Numerical Abstraction consists in 
abstracting the character of the difference from 
which plurality arises, retaining merely the fact. 
When I speak of three men I need not at once 
specify the marks by which each may be known 
from each. Those marks must exist if they are 
really three men and not one and the same, and 
in speaking of them as many I imply the exist- 
ence of the requisite differences. Abstract 
number, then, is the empty form of difference ; 
the abstract number three asserts the existence 
of marks without specifying their kind. Num- 
erical abstraction is thus seen to be a different 
process from logical abstraction, for in the latter 
process we drop out of notice the very existence 
of difference and plurality. . . . The ori- 
gin of the great generality of number is now ap- 
parent. Three sounds differ from three colours, 
or three riders from three horses ; but they agree 
in respect of the variety of marks by which they 
can be discriminated. The symbols 1 + 1 + 1 are 



^1-i ox THE i^"ATUHE OF 

tliiis the empty marks asserting the existence of 
discrimination. But in dropping out of sight 
the character of the differences we give rise to 
new agreements on which mathematical reason- 
ing is founded. . . . The common distinc- 
tion between concrete and abstract number can 
now be easily stated. In proportion as we speci- 
fy the logical characters of the things numbered, 
we render Ihem concrete. In the abstract num- 
ber three there is no statement of the points in 
which the three objects agree ; but in three coins, 
three men, or three horses, not only are the ob- 
jects numbered, but their nature is restricted. 
Concrete number thus implies the same con- 
sciousness of difference as abstract number, but 
it is mingled with a groundwork of similarity 
expressed in the logical terms. There is identity 
so far as logical terms enter ; difference so far as 
the terms are merely numerical. The reason 
of the important Law of Homogeneity will now 
be apparent. This law asserts that in every 
arithmetical calculation the logical nature of the 
things numbered must j'emain unaltered. The 
specified logical agreement of the things must 
not be affected by the unspecified numerical 
differences. A calculation would be palpably 
absurd which, after commencing with length, 
gave a result in hours. It is equally absurd, in 
a purely arithmetical point of view, to deduce 
areas from the calculation of lengths, masses 
from the combination of volume and density, or 
mofnenta from mass and velocity. It must re- 
main for subsequent consideration to decide in 



SUBJECT-MATTER. 215 

what sense one may truly say that two linear 
feet multiplied by two linear feet give four su- 
perficial feet ; arithmetically it is absurd, be- 
cause there is a change of unit. As a general 
rule we treat in each calculation only objects of 
one nature. A\'e do not, and cannot properly 
add, in the same sum yards of cloth and pounds 
of sugar. AVe cannot even conceive the result 
of adding area to velocity, or length to density, 
or weight to value. The units added must have 
a basis of homogeneity, or must be reducible to 
some common denominator. Nevertheless it is 
possible, and in fact common, to treat in one 
complex calculation the most heterogeneous quan- 
tities, on the condition that each kind of object 
is kept distinct, and treated numerically only in 
conjunction with its own kind. Different units, 
so far as their logical differences are specified, must 
never be substituted one for the other. {Ibid., 
pp. 158-60.) 

"Abstractly considered, Number is the measure 
of the relation between quantities or things of the 
same kind. We can form no conception of the 
absolute magnitude of any quantity, and can only 
acquire a relative conception of it, by comparing 
it with some other quantity of the same kind, 
assumed as a standard of comparison. The 
comparison is made by seeking how many times 
the standard is contained in the quantity mea- 
sured. The result of this comparison is a 
number." (Davies and Peck, Diet, of Math.) 

" Groups of units are what we really treat in 
arithmetic. The number five is really 1 -|- 1 -|- 1 



'216 OK THE NATURE OF 

+ 1 + 1 , but for tlie sake of conciseness we sub- 
stitute the more compact sign 5, or the name 
five. Tiiese names being* arbitrarily imposed in 
any one manner, an infinite variety of relations 
spring up between tbem which are not in the 
least arbitrary. If we define four as 1 + 1 + 1 + 1, 
and five as 1 + 1 + 1+1 + 1, then of course it 
follows that five=four + l ; but it would be 
equally possible to take this latter equality as a 
definition, in which case one of the former equali- 
ties would become an inference. It is hardly re- 
quisite to decide how we define the names of 
numbers, provided we remember that out of the 
infinitely numerous relations of one number to 
others, some one relation expressed in an equali- 
ty must be a definition of the number in question 
and the other relations immediately become nec- 
essary inferences. 

" in the science of number the variety of 
classes which can be formed is altogether infinite, 
and statements of perfect generality may be 
made subject only to diflSculty or exception at 
the lower end of the scale. Every existing 
number for instance belongs to the class M + 7 ; 
that is, every number must be the sum of another 
number and seven, except of course the first six 
or seven numbers, negative quantities not being 
here taken into account. Every number is the 
half of some other, and so on. The subject of 
generalization, as exhibited in mathematical 
truths, is an infinitely wide one. In number 
we are only at the first step of an extensive series 
of generalizations. As number is general com- 



SUBJECT-MATTER. 217 

pared witli the particular things numbered, so 
we have general symbols for numbers, and gen- 
eral symbols for relations between imdetermined 
numbers. There is an unlimited hierarchy of 
successive generalizations." (Jevons, Pr. Sc, 
•p]), 167-168.) 

** A large proportion of the mathematical 
functions which are conceivable have no applica- 
tion to the circumstances of this world. Phy- 
sicists certainly do investigate the nature and 
consequences of forces which nowhere exist. 
Newton's Principia is full of such investigations. 
In one chapter of his Mecanique, Celeste Laplace 
indulges in a remarkable speculation as to what 
the laws of motion would have been if momen- 
tum, instead of varying simply as the velocity, 
had been a more complicated function of it. 
Thought is not bound down to the limits 
of what is materially existent, but is circum- 
scribed only by those Fundamental Laws of 
Identity, Contradiction, and Duality, which have 
already been laid down;" (Ibid., pp. 70-45.) 

205. ** Mathematical Judgments may be di- 
vided into two kinds — indemonstrable or axiom- 
atic judgments, whose necessity is self-evident ; 
and demonstrable judgments, whose necessity 
depends on some previous assumption. The 
necessity of the latter is derived from that of the 
former, so that the indemonstrable judgments 
alone require a special examination. Under 
this class are comprehended the axioms of geom- 
etry, properly so-called — ^viz., the original as- 
sumptions concerning magnitudes in space as 



218 01^ THE ]!{ATURE OF 

sucli, and tlie propositions belonging to the fun- 
damental operations of arithmetic — addition and 
subtraction. (Distinguish between postulates, and 
some axioms which are logical, not geometrical 
principles, and depend solely on the laws of 
thought.) (Though in some things, as in num- 
bers, besides adding and subtracting, men name 
other operations, as multiplying and dividing, 
yet are they the same ; for multiplication is but 
adding together of things equal ; and division 
but subtractino- of one thino- as often as we can. 
Ilobbes, Leviathan, p. i., chap. 5.) The ne- 
cessity of these judgments results from the exist- 
ence in the mind of the a -priori forms of intui- 
tion — Space and Time. The axioms of geometry 
are self-evident statements concerning magni- 
tudes in space ; such as that two straight lines 
cannot enclose a space. Their self-evidence or 
necessity is to be explained by the circumstance 
that the presented intuition, as well as the repre- 
sentative thought, is derived from within, not 
from without. For geometrical propositions are 
primarily necessary, not as truths relating to ob- 
jects without the mind, but as thoughts relating 
to objects within : their necessity, as regards 
real objects, is only secondary and hypothetical. 
If there exist anywhere in the world two perfect 
straight lines, those lines cannot enclose a space ; 
but if such lines exist nowhere but in my imagi- 
nation, it is equally true that I cannot think of 
them as invested with the contrary attributes. 
This necessity of thought is dependent on a cor- 
responding necessity of intuition. The object 



SUBJECT-MATTER. 319 

of whicli pure geometry treats is not dependent 
on sensation, but sensation on it : it is a condi- 
tion under whicli alone sensible experience is 
possible ; and therefore its characteristics must 
accompany all our thoughts concerning any pos- 
sible object of such experience ; for, however 
much we may abstract from the attributes of 
this or that particular phenomenon of experience, 
we are clearly incompetent to deprive it of those 
conditions under which alone, from the consti- 
tution of our minds, experience itself is possible. 
We can perceive only as we are permitted by 
the laws of our perceptive faculties, as we can 
think only in accordance with the laws of the un- 
derstanding. If, then, by a law of my percep- 
tive faculty, I am compelled to regard all ob- 
jects as existing in space, the attributes which 
are once presented to me as the properties of a 
given portion of space, such as the pair of 
straight lines now present to my sight or imagi- 
nation, must necessarily be thought as existing 
in all space and at all times. For to imagine a 
portion of space in which such properties are 
not found, would not be to imagine merely a 
different combination of sensible phenomena, 
such as continually takes place without any change 
in the laws of sensibility : it would be to imagine 
myself as perceiving under other conditions than 
those to which, by a law of my being, I am sub- 
jected. But a condition, though potentially ex- 
isting in the original constitution of the mind, 
is actually manifested only in conjunction with 
that of which it is the condition. Space, there- 



220 Oiq- THE KATUKE OF 

fore, and its laws, are first made known to con- 
sciousness on the occasion of an actual phenom- 
enon of sense. Hence the twofold character of 
geometrical principles : empirical, as suggested 
in and through an act of experience ; necessary, 
as relating to the conditions under which alone 
such experience is possible to human faculties. 

" Arithmetic is related to Time as Geometry 
to Space ; and the necessity of its propositions 
may be explained upon similar principles. The 
two sciences, however, present some important 
features of distinction. Most of the proposi- 
tions of geometry are deductive : it contains 
very few axioms, properly so called, and its pro- 
cesses consist in the demonstration of a multi- 
tude of dependent propositions from the combi- 
nation of these axioms with certain logical prin- 
ciples of thought in general. On the other 
hand, the fundamental operations of arithmetic 
— addition and subtraction — present to us a vast 
number of independent judgments, every one of 
which is derived immediately from intuition, 
and cannot, by any reasoning process, be de- 
duced from any of the preceding ones. (Although 
it is simpler to regard addition and subtraction 
as independent processes, yet no result of either 
can be derived from a preceding result of the 
same operation.) Pure geometry cannot advance 
a step without demonstration, and its processes 
are therefore all reducible to the syllogistic form. 
Pure arithmetic contains no demonstration ; 
and it is only when its calculus is applied to the 
solution of particular problems that reasoning 



SUBJECT-MATTER. 221 

takes place, and the laws of the syllogism be- 
come applicable. It is not reasoning which tells 
us that two and two make four ; nor, when we 
have gained this proposition, can we in any way 
deduce from it that two and four make six. 
We must have recourse, in each separate case, 
to the senses or the imagination (memory), and 
by counting up the individual succession corre- 
sponding to each term, intuitively perceive the 
resulting sum. The intuition thus serves nearly 
the same purpose as the figure in a geometrical 
demonstration ; with the exception that, in the lat- 
ter case, the construction is adopted to furnish pre- 
mises to a proposed conclusion ; while in the for- 
mer it gives us a judgment which we have no im- 
mediate intention of applying to any further use. 
*' The intuition in the case of arithmetic is 
furnished by the consciousness of successive 
states of our own minds. Setting aside all other 
characteristics of those states, save that of their 
succession in time, we have the immediate con- 
sciousness of one, two, three, four, etc. A 
purely natural arithmetic would consist in carry- 
ing on this series, with no other relation between 
its members but that of succession, until the 
memory became unable to continue the process. 
The artificial methods by which calculation is fa- 
cilitated and extended, such as that of a scale of 
notation, in which the series recommences after 
a certain number of members, vastly increase the 
utility of the calculus, but do not affect its psy- 
chological basis. To construct the science of 
arithmetic in all its essential features, it is only 



222 OK THE Is^ATURE OF 

necessary that we should be conscious of a suc- 
cession in time, and should be able to give names 
to the several members of the series ; and since 
in every act of consciousness we are subject to 
the condition of succession, it is impossible in 
any form of consciousness to represent to our- 
selves the facts of arithmetic as other than they 
are. 

" The necessity of propositions in geometry 
and arithmetic is thus derived from their relation 
to the universal forms of intuition — Space and 
Time. We can suppose the possibility of be- 
ings existing whose consciousness has no relation 
to space or time at all. This is no more than to 
admit the possible existence of intelligent beings 
otherwise constituted than ourselves, and conse- 
quently incomprehensible by us. But to sup- 
pose the existence of geometrical figures or arith- 
metical numbers such as those with which we 
are now acquainted, is to suppose the existence 
of space and time as we are now conscious of 
them, and therefore relatively to beings whose 
mental constitution is so far similar to our own. 
Such a supposition necessarily carries with it all 
the mathematical relations in which space and 
time, as given to us, are necessarily thought. 
For mathematical judgments strictly relate only 
to objects of thought as existing in my mind, 
not to distinct realities existing in relation to my 
mind. They therefore imply no other exist- 
ence than that of a thinking subject, modified 
in a certain manner. Destroy this subject, or 
change its modification, and we cannot say, as 



SUBJECT-MATTER. 223 

in otlier cases, that the object may possibly exist 
still without the subject, or may exist in a new 
relation to a new subject ; for the object exists 
only in and through that particular modification 
of the subject, and, on any other supposition, is 
annihilated altogether. Thus it is impossible to 
suppose that a triangle can, in relation to any 
intelligence whatever, have its angles greater or 
less than two right angles, or that two and two 
should not be equal to four ; though it is quite 
possible to suppose the existence of intelligent 
beings destitute of the idea of a triangle or of 
the number two. This is a necessary matter 
in the strict sense of the term ; a relation which 
our own minds are incapable of reversing, not 
merely positively, in our own acts of thought, 
but also negatively, by supposing others who 
can do so." (Mansel, Metaphjsics, pp. 226-81, 
ed. 1871.) 

206. " The main branches of mathematical 
science w^ere formerly stated to be arithmetic and 
geometry, springing out- of the simple notions 
of number and space. This is too limited a de- 
scription. Unquestionably the science of num- 
bers, strictly and demonstratively treated, and 
that of geometry, or the deduction of the ele- 
mentary properties of figure from definitions 
which are entirely exclusive of numerical consid- 
erations, must be considered as the elementary 
foundations, but not as the ultimate divisions, of 
mathematics. To them we must add the science 
of operation, or algebra in its widest sense, — the 
method of deducing from symbols which imply 



224, OK THE KATUEE OF 

operations on magnitude, and which are to be 
used in a given manner, the consequences of the 
fundamental definitions. The leading idea of 
this science is operation or process, just as num- 
ber is that of arithmetic, and space and figure of 
geometry : it is of a more abstract and refined 
character than the latter two, only because it does 
not immediately address itself to the notions 
which are formed in the common routine of life. 
It is the most exact of the exact sciences, accord- 
ing to the idea of their exactness which frequent- 
ly entertained, being more nearly based upon 
definition than either arithmetic or geometry. 
It is true that the definitions must be such as to 
present results which admit of application to 
number, space, force, time, &c., or the science 
would be useless in mathematics, commonly so 
called ; but it is not the less true that a system 
of methods of operation, based upon general 
definitions, and conducted by strict logic, may 
be made to apply either to arithmetic or geome- 
try, according to the manner in which the gen- 
eralities of the definition are afterwards made 
specific." {English Cydopcedia, Mathematics.) 
207. *' The methods of observation of quan- 
tity in general are^ Numeration, which is pre- 
cise by the nature of number ; the Measurement 
of Space and Time, which are easily made pre- 
cise ; the Conversion of Space and Time, by 
which each aids the measurement of the other ; 
the Method of Repetition ; the Method of Coinci- 
depce or Ipterferences. ' ' (Whewell, Nov. Org, 
Jlen, p. 145.) 



SUBJECT-MATTER. 225 

208. The branches known as the Natural Sci- 
ences can be taught by Object Teaching in so 
far as facts are needed and can be observed, for 
the things shown or observed are the immediate 
objects to be learned. History cannot, from its 
nature, be taught objectively, except it happen 
that the learner can be an eyewitness of the 
events narrated. Language and Literature can 
be taught by Object Teaching, they being ends 
unto themselves, and subjects of inspection. 
Applied mathematics, being themselves illustra- 
tions, can hardly be taught illustratively. 

209. As soon as perception and determina- 
tion have given to the mind knowledge of indi- 
vidual facts, the power of retention holds them 
for future use — they are reproduced and repre- 
sented in consciousness where Thought seizes 
them, and constructs science from them. When 
knowledge of individual objects is gained, the^ 
usefulness of the objects ceases. All beyond is 
a work of the power of Thought. Hence the 
stages, for subject matter that will admit of it, 
are : — (1) Knowledge of facts obtained by Per- 
ception and Discrimination, which is the prov- 
ince of Object Teaching ; (2) The activity of 
Thought upon this knowledge, aided as it may 
be by Imagination. In this second stage. Ob- 
jects are rather a hindrance if present than an 
aid, because they are so much useless material 
that should be put aside — Perception has done 
its work, Discrimination has separated, and now 
the senses may slumber while Thought is rearing 
science out of similarities and identities — any 



236 OK THE NATURE OF 

energy of attention wliicli is diverted, at tliis 
time, towards the objects themselves is so much 
abstracted from Thought, wliich is thereby weak- 
ened, and Science so much endangered, for Sci- 
ence is not possible without Thought. 

' ' A real experiment is a very valuable product 
of the mind, requiring great knowledge to invent 
it and great ingenuity to carry it out. 
It may be said that a boy takes more interest in 
the matter by seeing for himself, or by perform- 
ing for himself, that is by working the handle 
of the air-pump : this we admit, while we con- 
tinue to doubt the educational value of the trans- 
action. . . . The function of experiment, 
properly so called, in the investigation of the 
laws and processes of nature can hardly be unduly 
exalted ; but it may be said of the experimenter, 
as of the poet, that he is born and not manufac- 
tured." (I. Todhunter, Conflict of Studies, ^^. 
16-19.) 

210. Ignorance of the province of Object 
Teaching leads to disaster, in practice, in mental 
discipline. This teaching addresses the attention 
of Perception and Discrimination. Then the ob- 
jects have served their purpose. If the knowl- 
edge of facts which the learner has obtained be 
not wrought up by Thought into Concepts, which 
are general in their character and form the data 
for Reasoning, his mind is left far short of dis- 
cipline. For true intellectual power comes only 
by constant exercise of Thought, and Thought 
busies itself only with mental products. Neglect 
of demanding maximum amounts of work for 



SUBJECT-MATTEK. 227 

the powers of Thought of pupils habituates them 
to superficial scholarship — they may be apt at 
observing, when objects are placed before them, 
but they will develop little power of independent 
research, of vigorous appUcation to thinking, or 
of the power to generalize. The mere acquisi- 
tion and memorizing of a number of isolated, 
heterogeneous, or unrelated facts, is neither learn- 
ing nor discipline, whether the facts are obtained 
from personal observation and examination, from 
oral statements of teachers, or gleaned from 
books. 

(c) ON DISCOVERING METHODS OF TEACHING 
SPECIAL SUBJECTS. 

211. Having outlined the powers of know- 
ing and the nature of subject-matter, it yet re- 
mains to investigate the Methods of Teaching, 
when they are to be applied in the teaching of 
any given subject. " In every Treatise upon 
any Science two Points are indispensably re- 
quired ; the First, that the science which is the 
subject of it be fully explained ; the second, 
. . . that plain Directions be given, how and 
by what method such science may be attained." 
(Longinus, On The Sublime, pp. 1-2, Tr. by 
Wm. Smith, 1*739, London.) It is not the 
purpose of this discussion to develop a complete 
Method and Mode in any subject — simply to 
present the magnitude, importance, and direction 
in general, of Methods in special studies. To 
discover a Method to teach any branch is no 



228 Olf DISCOVERING METHODS OF 

easy task. The exact psychological faculties to 
be addressed are often difficult to name — the 
subject-matter must be maintained in its integrity 
while it is manipulated into a system to suit the 
capacities of the mind taught. This latter point 
is all important, as it sometimes happens that 
the truths of science are sacrificed to error when 
they appear in Modes of Teaching. It often 
happens that systems, in their steps or degrees 
of advancement, do only scant justice to the 
mind to be taught, because they are too diffuse, 
too prolix, too narrow in their steps, or too in- 
elastic. These faults of systems are grave ones, 
and show the teacher uninformed concerning 
Methods of Teaching. The subject-matter 
should be properly divided and subdivided, but 
never below the present attainments of the 
learner, for mind grows from reaching out after 
the unknown and the diflflcult, provided it be not 
clouded by discouragement in the pursuit. The 
subject-matter should be carefully freed from all 
that is not to be learned in that lesson — the 
steps to be presented should be those which are 
vital to the system of the subject taught. Too 
many words and points, and too much related 
subject-matter, distract the mind of the learner 
so that the real and vital points are only dimly 
apprehended. He is most fortunate in the class- 
room who sets forth, in sharp outline, just the 
maximum of subject-matter for his class — in- 
spiring a zeal and determination for an increased 
power on the morrow's lesson. 

212. Suppose that a teacher wishes to dis- 



TEACHIl^G SPECIAL SUBJECTS. 229 

cover the Method of Teaching children the pro- 
cess of Adding Numbers. How, in practice, 
shall he proceed ? 

1. Concerning the nature of the subject-mat- 
ter : 

(a) Addition, being purely mathematical 
in its nature, is incapable of being 
presented by Object Teaching. 

(6) Being capable of a hypothetical ap- 
plication to material objects, it can be 
taught by Illustrative Teaching. 

(c) The numbers to be added together 
are but so many forms for the aggre- 
gate of many smaller parts, having no 
logical connection. 

(cT) The subject-matter is represented by 
certain characters called Figures, 
which are arbitrary in their form, and 
have no logical connection with each 
other. 

2. Concerning the faculties of mind that are 
primarily active in learning addition : 

(a) The Perceptive faculties are required 
to note, intuitively, the individuals 
that are presented to them. 

(b) Discrimination, or Comparison, dis- 
tinguishes one individual in Conscious- 
ness from another. 

(c) Memory in general, or, according to 
Hamilton, Retentiveness (or Mem- 
ory), Recollection (or Reproduction), 
and Representation, preserves for fu- 
ture use the knowledge obtained 



230 OK DISCOVERING METHODS OF 

tlirough Perception and Discrimina- 
tion. 
{d) The Power of Detecting Identity, or 
the Power of Comparison, or the 
Power of Thought, compares or iden- 
tifies what may come within Conscious- 
ness througli Perception, with what 
may come there through Memory. 
(e) The Power of expressing Thought, or 
Language. 
3. Having discovered these principles, which 
are the Method of Teaching addition, he pro- 
ceeds to invent his Mode of Teaching addition. 
This Mode may be by illustration, by telling, by 
questioning, and the like. 

213. He regards these particular points : 1. 
To what degree of power are the faculties of these 
children grown ? 2. Is this System of Addition 
philosophically constructed ? 3. In what quan- 
tity of subject-matter shall the points of the sys- 
tem be set to these faculties ? He may write 
out the complete lesson, as he proposes to pre- 
sent it. This is his Mode. He may then ap- 
pear before the clasc to teach. His individual- 
ity, when presenting the subject-matter, exhibits 
his Manner. 

The only guide possible for procedure in the 
case is the intelligence of the teacher, who now 
invents the Mode. If there be deficiency here, 
it will be no matter for surprise if the children 
are poorly taught. 

When a System of subject-matter is arranged 
in detail in Modes of Teaching it, the arrange- 



TEACHIi^G SPECIAL SUBJECTS. 23i 

ment is called Methodical. All methodical dis- 
cussions for teaching must rest upon Methods of 
Teaching. 

214. In the foregoing procedure, the dis- 
covering of the Method of Teaching — the process 
of discovering the faculties, and the nature of 
the subject-matter that is to be adjusted to them, 
comprised under (1) and (2) — is the conception 
of the Science of Teaching. 

215. The Invention of the Mode of Teaching, 
together with the Manner of exhibiting it in 
practice, is the conception of the Art of Teach- 
ing. 

216. The Investigation of the Science and 
the Art of Teaching constitutes the Conception 
of the Profession of Teaching. 



m. 

CONCLUDING REFLECTIONS. 

217. Whatever qualifications of mind and 
person the teacher may have, he is still lacking 
in a most important element of success if he has 
not a, quick apprehension of adopting means to 
ends. He must possess versatility of powers to 
discover Methods of Teaching, in order to invent 
Modes by which he shall incite to activity the 
pupil's mind with certainty. To do this, he 
needs a large stock of *' That unacquired, un- 
bought, untaught sagacity, which certain men 
have by nature," called Common Sense or good 
sense. (McCosh, Int. of Mind, p, 93, ed. 1870.) 
*' Common Sense is the spontaneous action of 
right reason." (M. Bautain, Art of Ext. Speak- 
ing, ed. 1871.) This ability is needed nowhere 
more than in the school-room, and he who lacks 
it should diligently apply himself to cultivating 
his ' ' good sense, " if he would attain eminence 
in the Profession of Teaching. 

218. "An open-eyed and open-minded 
physician keeps adding to his knowledge and 
altering and widening his theories to the day of 
his death ; there is not less to be learned in the 
world of mind — in the world of the school-room. 



CON"CLUDIKG REFLECTIONS. 233 

The kind of teacher who stiffens into 
the school-master misses his opportunities, or falls 
a victim to that arrestment of development which 
has overtaken many school subjects, and which 
sometimes overtakes the whole of school life." 
(Meiklejohn, Inaugural Address, Bell Chair of 
Education, p. 11, 1876, Edinburgh.) 

219. " Intellectually, as well as morally, he 
(Arnold) felt that the teacher ought himself to be 
perpetually learning, and so constantly above the 
level of his scholars. ' I am sure,' he said, 
speaking of his pupils at Laleham, ' that I do 
not judge of them or expect of them, as I should, if 
I were not taking pains to improve my own mind. ' 
For this reason he maintained that no school- 
master ought to remain at his post much more 
than fourteen or fifteen years, lest, by that time, 
he should have fallen behind the scholarship of 
the age ; and by his own reading and literary 
M^orks he endeavored constantly to act upon this 
principle himself. . . . ' The dangers ' (of 
falling behind), he observed, ' were of various 
kinds. One boy may acquire a contempt for the 
information itself, which he sees possessed by a 
man whom he feels nevertheless to be far below 
him. Another (pupil) will fancy himself as 
much above nearly all the world as he feels he is 
above his own tutor, and will become self-suffi- 
cient and scornful. A third will believe it to be 
his duty, as a point of humility, to bring himself 
down intellectually to a level with one whom he 
feels bound to reverence ; and thus there have 
been instances where the veneration of a young 



234 COi^CLUDIITG REFLECTIOI^S. 

man of ability for a teacher of small powers has 
been like a millstone round the neck of an eagle. ' ' ' 
(Arnold, Life of, p. 137, ed. 1870.) 

220. " We may say that common sense 
scarcely claims to provide more than rather in- 
definite general rules, which no prudent man 
should neglect without giving himself a reason 
for doing so. Such reasons may either be drawn 
from one's knowledge of some peculiarities in 
one's nature, or from the experience of others 
whom one has ground for believing to be more 
like oneself than the average of mankind are. 
For though, as we saw, there is considerable 
risk of error in thus appropriating the experience 
of others — and in fact the expression of it will 
sometimes appear to be as hesitating and contra- 
dictory as the judgments of common sense — we 
may extract from it counsel sufficiently consist- 
ent and authoritative to supplement at least 
roughly the deficiencies of our own empirical 
generalizations. ' ' (Sidgwick, Methods of Ethics ^ 
p. 145, ed. 1874.) 

ZZl. " But many who allow the use of sys- 
tematic principles in other things, are accustomed 
to cry up Common-Sense as the sufficient and 
only safe guide in Reasoning. Now by Common- 
Sense is meant, I apprehend, (when the term is 
used with any distinct meaning,) an exercise of 
the judgment unaided by any Art or system of 
rules : such an exercise as we must necessarily 
employ in numberless cases of daily occurrence ; 
in which, having no established principles to 
guide us, — no line of procedure, as it were, dis- 



COKCLUDIIS'G KEFLECTIONS. 235 

tinctly chalked out — we must needs act on the 
best extemporaneous conjectures we can form. 
He who is eminently skilful in doing this, is said 
to possess a superior degree of Common-Sense. 
But that Common-Sense is only our second best 
guide — that the rules of Art, if judiciously 
framed are always desirable when they can be 
had, is an assertion, for the truth of which I may 
appeal to the testimony of mankind in general ; 
which is so much the more valuable, inasmuch 
as it may be accounted the testimony of adver- 
saries. For the generality have a strong predi- 
lection in favor of Common- Sense, except in 
those points in which they, respectively, possess 
the knowledge of a system of rules ; but in these 
points they deride any one who trusts to unaided 
Common-Sense. " A sailor e.g. will, perhaps, 
despise the pretensions of medical men, and 
prefer treating a disease by Common-Sense : but 
he would ridicule the proposal of navigating a 
ship by Common-Sense, without regard to the 
maxims of nautical art. A physician, again, 
will perhaps contemn Systems of Political- 
Economy, of Logic, or Metaphysics, and insist 
on the superior wisdom of trusting to Common- 
Sense in such matters ; but he would never ap- 
prove of trusting to Common-Sense in the treat- 
ment of diseases. 

" Neither, again, would the Architect recom- 
mend a reliance on Common-Sense alone, in build- 
ing, nor a Musician, in music, to the neglect of 
those systems of rules, which, in their respective 
arts have been deduced from scientific reason- 



336 CONCLUDING REFLECTIONS. 

ing aided by experience. And the induction 
might be extended to every department of prac- 
tice. Since, therefore, each gives the preference 
to unassisted Common-Sense only in those cases 
where he himself has nothing else to trust to, 
and invariably resorts to the rules of art, wher- 
ever he possesses the knowledge of them, it is 
plain that mankind universally bear their testi- 
mony, though unconsciously and often unwill- 
ingly, to the preferableness of systematic knowl- 
edge to conjectural judgments. 

" There is, however, abundant room for the 
employment of Common-Sense in the application 
of the system. To bring arguments out of the 
form in which they are expressed in conversation 
and in books, into the regular logical shape, must 
be of course, the business of Common-Sense, 
aided by practice, for such arguments are, by 
supposition, not as yet within the province of 
science." (Whi\ie]y, JElements of Logic y 1859, 
pp. xi.-xii. of Preface.) 

222. " The one talent Avhich is worth all 
other talents put together in all human affairs is 
the talent of judging right upon imperfect ma- 
terials, the talent if you please of guessing 
right. It is a talent which no rules will ever 
teach and which even experience docs not al- 
ways give. It often coexists with a good deal 
of slowness and dulness and with a very slight 
power of expression. All that can be said about 
it is, that to see things as they are, without exag- 
geration or passion, is essential to it ; but how 
can we see things as they are ? Simply by open- 



COKCLUDIN"G KEFLECTIOKS. 237 

ing our eyes and looting with whatever power 
we may have." (Stephen, Liberty, Equality, 
Fraternity, p. 352, ed. 1874, London.) 

223. '' The assumed logical perfection of 
thought bears about the same relation to the or- 
dinary state of the human mind as the assump- 
tion of perfectly rigid levers and perfectly flexible 
cords bears in the action of those instruments in 
practice. But, on the other hand, the possibility 
of making such allowances implies that the differ- 
ence between practice and theory is one of de- 
gree only, and not of kind. The instrument as 
used may not be identical with the instrument 
as contemplated, but it must be supposed cap- 
able of approximation to it." (Mansel, Prol. 
Log., p. 17.) ^ 

224. " It is a common notion, or at least it 
is implied in many common modes of speech, 
that the thoughts, feelings, and actions of sen- 
tient beings are not a subject of science, in the 
same strict sense in which this is true of the ob- 
jects of outward nature. This notion seems to 
involve some confusion of ideas, which it is 
necessary to begin by clearing up. Any facts 
are fitted, in themselves, to be a subject of 
science which follow one another according to 
constant laws, although those laws may not have 
been discovered, nor even be discoverable by our 
existing resources. . . . Scientific inquiry 
has not yet succeeded in ascertaining the order 
of antecedence and consequence among phenom- 
ena, so as to be able, at least in our regions of 
the earth, to predict them with certainty, or 



238 COKCLUDIiq^G REFLECTIONS. 

even with a high degree of probability. . . . 
But meteorology not only has in itself every 
natural requisite for being, but actually is, a 
science ; though the science is extremely imper- 
fect. . . . No one doubts that Tidology 
(as Dr. Whewell proposes to call it) is really a 
science. , . But circumstances of a local or casual 
nature, such as the configuration of the bottom 
of the ocean, the degree of confinement from 
shores, the direction of the wind, etc. , influence, 
in many or all places, the height and time of 
the tide ; and a portion of these circumstances be- 
ing either not accurately knowable, not precisely 
measurable, or not capable of being certainly 
foreseen, the tide in known places commonly 
varies from the calculated result of general prin- 
ciples by some difference that we are not able to 
foresee or conjecture. . . . And this is what 
is or ought to be meant by those who speak of 
sciences which are not exact sciences. As- 
tronomy was once a science, without being an 
exact science. ... It has become an exact 
science. . . . The science of human nature 
is of this description. It falls far short of the 
standard of exactness now realized in Astron- 
omy ; but there is no reason that it should not be 
as much a science as Tidology is, or as Astronomy 
was when its calculations had only mastered the 
main phenomena, but not the perturbations. 

" The phenomena with which this science of 
(human) nature is conversant being the thoughts, 
feelings, and actions of human beings, it would 
have attained the ideal perfection of a science if 



COKCLUDIKG REFLECTIOKS. 239 

it enabled us to foretell how an individual would 
think, feel, or act throughout life, with the same 
certainty with which astronomy enables us to pre- 
dict the places and the occultations of the heavenly 
bodies. It need scarcely be stated that nothing 
approaching to this can be done. The actions of 
individuals could not be predicted with scientific 
accuracy, were it only because we can not fore- 
see the whole of the circumstances in which those 
individuals will be placed. But further, even in 
any given combination of (present) circum- 
stances, no assertion, which is both precise and 
universally true, can be made respecting the 
manner in which human beings will think, feel, 
and act. This is not, however, because every 
person's modes of thinking, feeling, and acting 
do not depend on causes ; nor can we doubt that 
if, in the case of any individual, our data could 
be complete, we even now know enough of the 
ultimate laws by which mental phenomena are 
determined, to enable us in many cases to pre- 
dict, with tolerable certainty, what, in the 
greater number of supposable combinations of 
circumstances, his conduct or sentiments would 
be. But the impressions and actions of human 
beings are not solely the result of their present 
circumstances, but the joint result of those cir- 
cumstances and of the characters of the individ- 
uals ; and the agencies which determine human 
character are so numerous and diversified (noth- 
ing which has happened to the person through- 
out life being without its portion of influence), 



240 CONCLUDING REFLECTIONS. 

that in the aggregate they are never in any two 
cases exactly similar. Kence, even if our science 
of human nature were theoretically perfect, that 
is, if we could calculate any character as we can 
calculate the orbit of any planet, from given data ; 
still, as the data are never all given, nor ever 
precisely alike in different cases, we could neither 
make positive predictions, nor lay down univer- 
sal propositions. 

" Inasmuch, however, as many of those effects 
which it is of most importance to render amena- 
ble to human foresight and control are deter- 
mined, like the tides, in an incomparably greater 
degree by general causes, than by all partial causes 
taken together ; depending in the main on those 
circumstances and qualities which are common 
to all mankind, or at least to large bodies of 
them, and only in a small degree on the idiosyn- 
crasies of organization or the peculiar history of 
individuals ; it is evidently possible with regard 
to all such effects, to make predictions which 
will almost always be verified, and general pro- 
positions which are almost always true. And 
whenever it is sufficient to know how the great 
majority of the human race, or of some nation 
or class of persons, will think, feel, and act, these 
propositions are equivalent to universal ones. 
For the purpose of political and social science 
this is sufficient. As we formerly remarked, an 
approximate generalization is, in social inquiries, 
for most practical purposes equivalent to an exact 
one ; that which is only probable when asserted 



COKCLUDIiq-G REFLECTIOITS. 241 

of individual human beings indiscriminately se- 
lected, being certain wlien affirmed of the char- 
acter and collective conduct of masses. 

"It is no disparagement, therefore, to the 
science of Human Nature, that those of its gen- 
eral propositions which descend sufficiently into 
detail to serve as a foundation for predicting 
phenomena in the concrete, are for the most part 
only approximately true. But in order to give 
a genuinely scientific character to the study, it 
is indispensable that these approximate generali- 
zations, which in themselves would amount only 
to the lowest kind of empirical laws, should be 
connected deductively with the laws of nature 
from which they result ; should be resolved 
into the properties of the causes on which the 
phenomena depend. In other words, the science 
of Human Nature may be said to exist in propor- 
tion as the approximate truths, which compose 
a practical knowledge of mankind, can be ex- 
hibited as corollaries from the universal laws of 
human nature on which they rest ; whereby the 
proper limits of those approximate truths would 
be shown, and we should be enabled to deduce 
others for any new state of circumstances, in an- 
ticipation of specific experience. . . . The 
proposition now stated is the text on which are 
based the ' Laws of Mind, ' and ' Ethology, or the 
science of the Formation of Character. ' ' ' (Mill, 
System of Logic, ^^. 586-596, 8°ed. 1874.) 



APPENDIX OF QUOTATIONS. 

SECTION PAGE 

225. Appendix A.— On Method 346 

226. B.— OnSystem 376 

227. C— On Analysis 380 

228. D.— On Synthesis 383 

229. E.— On Definition 385 

230. F.— On Abstraction 390 

231. G.— On Generalization 392 

233. H.— On Classification 393 

233. I.— On Induction 413 

234. J.— On Interpretation 473 

235. K.— On Deduction 478 



APPENDIX A. 

225. Extracts Showing the Use of the 
TERM Method. 

1. From Hedge's Logick, ed. 1854, pp. 149- 
150. 

Method, in logick, is a proper classification and 
arrangement of our thoughts on any subject, 
either to facilitate the discovery of new truths, 
or to assist us in communicating to others truths 
already known ; or, lastly, to enable us to preserve 
for future use the knowledge, which we have ac- 
quired. The disposition best adapted to the in- 
vestigation of truth is the analytick method; 
which is therefore denominated the method of 
invention ; and that which is best suited to the 
communication of knowledge, is the synthetick 
method, which for this reason has been called 
the method of instruction. In both of these 
methods, ideas are arranged in such order, as 
to exhibit their mutual connexions and relations. 

2. ^YomQoT^i^eQ''& Elements of Logic, ed. 1860, 
pp. 23-25. 

Method is the order and arrangement of facts 
to produce a certain result ; to establish new 
truth, to investigate old, and to explain and teach 
both. It is derived from the Greek jusO^odov ^ 



246 APPEKDIX A. 

wliicli denotes the way through which we arrive 
at a certain result. 

AVhatever steps are taken to make knowledge 
profitable, to reduce theory to practice, and to 
give clear and intelligible ideas of science, con- 
stitute Method. The extension of the term 
Method, it is evident, will differ according to 
the subject to which it is applied. 

The methods of investigation differ slightly 
for the different kinds of science, but may gen- 
erally be classified under two heads. Analysis 
and Synthesis, of which the former is generally 
used in the private investigation of truth, and 
the latter for the purposes of instruction. . . . 
We speak of the Method of a single science, 
or a Method which is applied to all — as in that 
which leads to the Classification of the sciences. 
In either investigation the division of Method 
into Analysis and Synthesis, is a just one, as 
both are used in either process. 

3. From Day's Elements of Logic^ ed. 1868, 
pp. 132-133. 

'* Method in general is the regulated procedure 
towards a certain end ; that is, a process governed 
by rules, which guide us by the shortest way 
straight towards a certain point, and guard us 
against devious aberrations. Now the end of 
Thought is Truth, Knowledge, Science — expres- 
sions which may here be considered as convert- 
ible. Science, therefore, may be regarded as the 
perfection of thought, and to the accomplishment 
of this perfection the Methodology of Logic 
must be accommodated and be conducive." 



APPEl^DIX A. 247 

But while Science, thus, is the proper end 
of all Thought, and Logical Method must have 
reference to Thought as its one end, it is still to 
be regarded only as the immediate end, which 
may, itself, be modified and controlled by still 
higher ends. In fact. Science or Truth may 
have its end either in itself — in the True, or 
in the Beautiful, or in the Right and Good ; 
and the Method of Thought will vary in some 
respects with this specific remoter end. Still 
further, the Method of Thought will vary with 
the more specific ends under each of these higher 
governing ends. We may deal with Thought for 
the purpose of acquiring knowledge, or for the 
purpose of communicating knowledge ; and the 
Method requisite for the Investigation of Truth 
will so far vary from the Method requisite for 
the Communication of Truth. 

In like manner the Method of Thought, as 
governed by the higher end of guiding to the 
Beautiful, will vary specifically, as the particular 
end is the Contemplation or the Creation of the 
Beautiful. 

So, too, we have a specific variation in the 
Method of Thought, where the governing idea is 
the Right or the Good, according as Subjective 
or Objective Rectitude or Goodness is the partic- 
ular end. 

It is sufficient to point out here these modi- 
fications of Logical Method in respect to these 
several general ends in thinking. The full, de- 
tailed consideration of them belongs either to 
modified Logic or to Applied or Special Logic. 



248 APPEN^DIX A. 

Pure Logic confines itself to the domain of Truth 
in itself — Science for its own sake. 

4. From Fleming's Vocabulary of Philosophy , 
ed. 1858, pp. 316-319. 

Method means the way or path by which we 
proceed to the attainment of some object or aim. 
In its widest acceptation, it denotes the means 
employed to obtain some end. Every art and 
every handicraft has its method. 

Scientific or philosophical method is the march 
which the mind follows in ascertaining or com- 
municating truth. It is the putting of our 
thoughts in a certain order with a view to im- 
prove our knowledge or to convey it to others. 

Method may be called, in general, the art 
of disposing well a series of many thoughts, 
either for the discovering truth when we are 
ignorant of it, or for proving it to others when 
it is already known. Thus there are two kinds 
of method, one for discovering truth, which is 
called analysis, or the method of resolution, and 
which may also be called the method of inven- 
tion ; and the other for explaining it to others 
when we have found it, which is called synthesis, 
or the method of composition, and which may 
also be called the method of doctrine. {Port 
Roy. Logic, Part IV., ch. 2.) 

"Method, which is usually described as the 
fourth part of Logic, is rather a complete prac- 
tical Logic. It is rather a power or spirit of the 
intellect, pervading all that it does, than its tan- 
gible product." (Thomson, Outline of Laws 
of Thought, sect. 119.) 



APPEiq-DIX A. 249 

Every department of pliilosophy has its own 
proper method ; but there is a universal method 
or science of method. This was called by Plato, 
dialectic ; and represented as leading to the true 
and real. (Bepub., \ih. vii.) It has been said 
that the word ^iOodoS, as it occurs in Aris- 
totle's Ethics, should be translated ' systems,' 
rather than ' method. ' — (Paul, Analysis of Aris- 
totWs Ethics, p. 1.) But the construction of 
a system implies method. And no one was more 
thoroughly aware of the importance of a right 
method than Aristotle. He has said [Metaphys., 
lib. ii.), '' that we ought to see v/ell what demon- 
stration (or proof) suits each particular subject ; 
for it would be absurd to mix together the re- 
search of science and that of method; two 
things, the acquisition of which offers great diffi- 
culty." The deductive method of philosophy 
came at once finished from his hand. And the 
inductive method was more extensively and suc- 
cessfully followed out by him than has been gen- 
erally thought. 

James Acontius, or Goncio, as he is sometimes 
called, was born at Trent, and came to England 
in 1567. He published a work, i)e Methodo. 
. According to him all knowledge de- 
duced from a process of reasoning presupposes 
some primitive truths, founded in the nature of 
man, and admitted as soon as announced ; and 
the great aim of method should be to bring these 
primitive truths to light, that by their light we 
may have more light. Truths obtained by the 



250 APPENDIX A. 

senses, and by repeated experience, become at 
length positive and certain knowledge. 

Descartes has a discourse on Method. lie 
has reduced it to four general rules. 

I. To admit nothing as true of which we 
have not a clear and distinct idea. We have a 
clear and distinct idea of our own existence. 
And in proportion as our idea of anything else 
approaches to, or recedes from, the clearness of 
this idea, it ought to be received or rejected. 

II. To divide every object inquired into as 
much as possible into its parts. Nothing is more 
simple than the ego, or self-consciousness. In 
proportion as the object of inquiry is simplified, 
the evidence -comes to be nearer that of self- 
consciousness. 

III. To ascend from simple ideas or cogni- 
tions to those that are more complex. The real 
is often complex : and to arrive at the knowledge 
of it as a reality, we must by synthesis reunite 
the parts which were previously separated. 

ly. By careful and repeated enumeration to 
see that all the parts are reunited. For the syn- 
thesis will be deceitful and incomplete if it do 
not reunite the whole, and thus give the reality. 

This method begins with provisory doubt, 
proceeds by analysis and synthesis, and ends by 
accepting evidence in proportion as it resembles 
the evidence of self-consciousness. 

These rules are useful in all departments 
of philosophy. But different sciences have 
different methods suited to their objects and to 
the end in view. 



APPENDIX A. 251 

In prosecuting science with the view of ex- 
tending our knowledge of it, or the Umits of it, 
we are said to follow the method of investigation 
or inquiry, and our procedure will be chiefly in 
the way of analysis. But in communicating 
what is already known, we follow the method of 
exposition or doctrines, and our procedure will 
be chiefly in the way of synthesis. 

In some sciences the principles or laws are 
given, and the object of the science is to discover 
the possible application of them. In these sci- 
ences the method is deductive, as in geometry. 
In other sciences, the facts or phenomena are 
given, and the object of the science is to dis- 
cover the principles or laws. In these sciences 
the proper method is inductive, proceeding by 
observation or experiment, as in psychology and 
physics. The method opposed to this, and 
which was long followed, was the constructive 
method ; which, instead of discovering causes by 
induction, imagined or assigned them a i^riori, 
or ex hypothesis and afterwards tried to verify 
them. This method is seductive and bold but 
dangerous and insecure, and should be resorted 
to with great caution. 

The use of method, both in obtaining and 
applying knowledge for ourselves, and in convey- 
ing and communicating it to others, is great and 
obvious. 

" Marshal thy notions into a handsome meth- 
od. One will carry twice as much weight, 
trussed and packed up in bundles, than when it 
lies untoward, flapping, and hanging about his 



25^ I»PEKDIX A. 

shoulders." {^Pleasures of Literature, 12mo, 
Lond., 1851, p. 104.) 

5. From Preface of ^^ A Brief English Gram- 
mar on a Logical Method,^ ^ by Alexander Bain, 

The chief peculiarity ia the plan of the pres- 
ent work lies in anticipating the unavoidable 
difficulties of the subject by a previous handling 
of certain elementary notions (belonging to all 
science), without which no one can hope to un- 
derstand the scope or method of grammar. 
After such preliminary explanations, I 
make no scruple to introduce a strict mode of 
defining the Parts of Speech. I also exemplify 
the leading subdivisions or classes of each. 
Moreover, I bring forward at once the equivalent 
phrases, which, in the case of the Adverb in par- 
ticular, are used more frequently than single 
words. On this method, the Grammatical pars- 
ing of a sentence directs attention forcibly to the 
meaning. ... It (the Key) also includes a 
large selection of additional examples, which are 
commented on with a view to set forth still far- 
ther the methods of parsing, and to illustrate 
the constructions and idioms of the language. 

6. From Whe well's Novum Organon Renova- 
tum, ed. 1858, pp. 141-144. 

The name Organon was applied to the works 
of Aristotle which treated of Logic, i.e., of the 
method of establishing and proving knowledge, 
and of refuting errour, by means of Syllogisms. 
Francis Bacon, holding that this method was in- 
sufficient for the augmentation of real knowl- 
edge, published his Novum Organon in which he 



APPEKDIX A, 253 

proposed for tliat purpose metliods from wliicli 
lie promised a better success, (p. 3.) 

The Methods by which the construction of 
Science is promoted are, Methods of Observa- 
tion, Methods of obtaining clear Ideas, and 
Metliods of Induction. 

Aphorism xxvii. ... I shall, therefore, 
attempt to resolve the Process of Discovery into 
its parts, and to give an account as distinct as may 
be of Rules and Methods which belong to each 
portion of the process. 

In Book II. we considered the three main 
parts of the process by which science is con- 
structed : namely, the Decomposition and Ob- 
servation of Complex Facts ; the Explication of 
our Ideal Conceptions ; and the Colhgation of 
Elementary Facts by means of those conceptions. 
The first and last of these three steps are capable 
of receiving additional accuracy by peculiar pro- 
cesses. They may further the advance of science 
in a more effectual manner, when directed by 
special technical Methods, of which in the pres- 
ent book we must give a brief view. In this 
more technical form, the observation of facts in- 
volves the Measurement of Phenomena ; and the 
Colligation of Facts includes all arts and rules by 
which the process of Induction can be assisted. 
Hence we shall have here to consider Methods 
of Observation, and Methods of Induction, us- 
ing these phrases in the widest sense. The sec- 
ond of the three steps above mentioned, the 
Explication of our Conceptions, does not admit 
of being much assisted by methods, although 



254 AP1>EKDIX A. 

something may be done by Education and Dis- 
cussion. 

The Methods of Induction, of which we ha\^e 
to speak, apply only to the first step in our 
ascent from phenomena to laws of Nature ; — the 
discovery of Laws of Phenomena. A higher and 
ulterior step remains behind, and follow in natu- 
ral order the discovery of Laws of Phenomena ; 
namely, the Discovery of Causes ; and this must 
be stated as a distinct and essential process in a 
complete view of the course of science. Again, 
when we have thus ascended to the causes of 
phenomena and of their laws, we can often rea- 
son downwards from the cause so discovered ; 
and we are thus led to suggestions of new phe- 
nomena, or to new explanations of phenomena 
already known. Such proceedings may be termed 
Applications of our discoveries ; including in 
the phrase. Verifications of our Doctrines by 
such an application of them to observed facts. 

Hence we have the following series of pro- 
cesses concerned in the formation of science. 

(1.) Decomposition of Facts ; 

(2.) Measurement of Phenomena ; 

(3.) Explication of Conceptions ; 

(4.) Induction of Laws of Phenomena ; 

(5.) Induction of Causes ; 

(6.) Application of Inductive Discoveries. 

Of these six processes, the methods by which 
the second and fourth may be assisted are here 
our peculiar object of attention. The treat- 
ment of these subjects in the present work must 
necessarily be scanty and imperfect, although we 



APPEKDIX A. 255 

may perhaps be able to add something to what 
has hitherto been systematically taught on these 
heads. Methods of Observation and of Induc- 
tion might of themselves form an abundant sub- 
ject for a treatise, and hereafter probably will do 
so, in the hands of future writers. A few_ re- 
marks, offered as contributions on this subject, 
may serve to show how extensive it is, and how 
much more ready it now is than it ever before 
was, for a systematic discussion. 

Of the above steps of the formation of sci- 
ence, the first, the Decomposition of Facts, has 
already been sufficiently explained in the last 
Book : for if we pursue it into further detail and 
exactitude, we find that we gradually trench upon 
some of the succeeding parts. I, therefore, pro- 
ceed to treat of the second step, the Measure- 
ment of Phenomena ;— of Methods by which 
this work, in its widest sense, is executed, and 
these I shall term Methods of Observation. 

Y. FromBowen's Logic, ed. 1874, pp. 30-38. 
Logic is the Science of the Necessary Laws of 
Pure Thought, . . . that is, it 'treats of 
Language so far only as this is the vehicle of 
Thought. Just the reverse is true of the science 
of Grammar, which treats primarily of Language, 
and only secondarily of Thought. Logic might 
be called the Grammar of Thought. . 
Pure, or, as it is sometinieis terinea, Formal 
Thought, is the mere process of thinking, irre- 
spective of what we are thinking about. It 
has already been said that the Acquisitive or 
Perceptive Faculty furnishes " the Matter," while 



256 APPENDIX A. 

the Understanding supplies '^ tlie Form," of our 
knowledge. This distinction between Matter 
and Form is one of considerable importance in 
the history of philosophy. The former is the 
crude material or the stuff of which anything 
consists, or out of which it is made ; while the 
latter is the peculiar shape or modification given 
to it by the artist, whereby it has become this 
particular thing which it is, and not something 
else which might have been fashioned out of the 
same substance. Thus, wood is the Matter of 
the desk on which I am writing, whilst the Form 
is that which entitles it to be called a desk, rather 
than a table or a chair. Vocal sound is the 
Matter of speech, and articulation is its Form. 
It is evident that these are two correlative no- 
tions, each of which implies the other : Matter 
cannot exist except under some Form, and there 
cannot be any Form except of some given Mat- 
ter. But though the two cannot actually be sep- 
arated, the mind can consider each separately 
through that process, called abstraction, whereby 
the attention is wholly given to the one to the 
exclusion of the other. We may think sepa- 
rately of the attributes which are common to a 
whole class of Forms, disregarding altogether, 
for the moment, the Matter of which each of 
them really consists. Borrowing algebraic 
symbols, the Matter in each case may be desig- 
nated by a letter of the alphabet, the peculiar 
significance of which is, that it stands for any 
Matter whatever, and not for any one in partic- 
ular. Thus, A is B, is the Form of an affirma- 



APPEI^DIX A. 257 

tive judgment, wherein A and B stand for any 
two Concepts whatever. Hence, whatever is true 
of the general formula, A is B, will be true also 
of any such particular instances, as Iron is mallea- 
ble, Trees aro plants, etc., wherein the Form is 
associated with some particular Matter. In say- 
ing, then, that Logic is concerned only with the 
Forms of Thought, or Pure Thought, or Thought 
in the abstract, — for all these expressions signify 
the same thing, — we mean only, that what is Ma- 
terial in Thought is extralogical, and, as logi- 
cians, we have nothing to do with it ; just as 
the geometer has nothing to do with the partic- 
ular diagram on the paper before him, except so 
far as it is a symbol, or universal Form, of all pos- 
sible figures of the same general character. . . . 

Ao-ain, the definition of Loo-ic assumes that 
the process of Thinking, like every other opera- 
tion in nature, does not take place at random, 
but according to certain fixed Laws or invariable 
modes of procedure. There could be no com- 
munication of Thought from one mind to an- 
other, if the process of Thinking in all minds 
were not subject to the same general rules. We 
follow these laws for the most part unconscious-' 
ly, as a distinct recognition of them is not by 
any means necessary for correct thinking ; just 
so, many persons speak and write correctly 
without any knowledge of the grammarian's 
rules. 

Properly speaking. Pure Logic terminates 
with the consideration of the three classes of 
products — namely, Concepts, Judgments, and 



358 APPENDIX A. 



Reasonings — which are the elements into which 
all Thought is resolved. But Thought itself is 
subsidiary to the attainment of knowledge, — that 
is, to Science. The question remains, then, 
after we have fully treated of Concepts, Judg- 
ments, and Reasonings, taken separately or con- 
sidered in themselves alone, what use is to be 
made of them, taken together, in the construc- 
tion of Science. A full answer to this question, 
as it would involve a study of the objects of 
Science, — that is, of the matter of the special 
sciences, — evidently falls outside of the province 
of Logic. But a partial answer to it, regarding 
Science in its relation, not to the objects known, 
but to the knowing mind, may be considered as 
a natural appendage to Logic, as it embraces the 
conditions not merely of possible, but of perfect, 
Thought. Such an answer is usually called the 
Doctrine of Method, or Logical Methodology. 
Pure Logic considers only the Necessary Laws 
to which all Thought must conform ; the Doc- 
trine of Method regards those rules and princi- 
ples to which all Thought ought to conform in 
order to obtain its end, which is the advance- 
ment of Science. Pure Logic treats merely of 
the elements of Thought, while Logical Method- 
ology regards the proper arrangement of these 
elements into an harmonious whole. All Method 
is a well-defined progress towards some end ; 
and the end in this case is the attainment of 
truth. Practically speaking, the Doctrine of 
Method is a body of rules or precepts looking to 
the proper regulation of the Thinking Faculty 



QUOTATIOl^S OIT METHOD. 259 

in the pursuit of knowledge ; and, as such, it 
necessarily lacks the precision and the demon- 
strative certainty which are characteristic of the 
principles of Pure Logic. The laws of Pure 
Thought are absolute ; the merits of Perfect 
Thought are various, and attainable in different 
deojrees, accordino; to circumstances. 

Another distinction has been taken, in this 
science, between Pure and Applied Logic, or as 
Sir William Hamilton prefers to call the latter. 
Modified Logic. The former, as we have seen, 
considers the Thinking Faculty alone, as if it 
constituted the whole of the human mind, and 
therefore as if its Laws and Products were unaf- 
fected by any collateral and disturbing influences, 
bat were manifested in precisely the same man- 
ner by different persons. It takes no account of 
the defects and hinderances which obstruct the 
normal action of the understanding. Modified 
Logic, on the other hand, considers Thought as 
it is, and not merely as it ought to be. It re- 
gards " the Causes of Error and the Impediments 
to Truth by which man is beset in the employ- 
ment of his Faculties, and what are the means 
of their removal." And yet it is a universal 
science, — as much so as Pure Logic ; — for it 
does not consider the Matter of Thought. 
. . . But Modified Logic is not properly called 
Logic, as it is a branch of Psychology, which 
treats of the phenomena of mind in general, and 
not merely of the norm.il action and necessary 
laws of one special faculty, the Understanding. 
As Modified Logic, however, is nearly allied in 



S60 QUOTATIOI^"S ON" METHOD. 

purpose with the Doctrine of Method, both look- 
ing to the same general end, — the attainment of 
truth through the proper regulation of the Think- 
ing Faculty, — the two may well be considered 
together, under the general name of Applied 
Logic, as a kind of supplement to the science 
properly so called. 

8. From Outlines of Ontological Science, by 
H. N. Day, ed. 1878, pp. 123 and following. 

The very conception of method involves, to- 
gether with something that changes, a source or 
orio^in from which the chano:e beo-ins ; an end or 
goal in which it rests or to which it tends ; and 
a way by which the end is reached from the be- 
ginning. 

A rational method, moreover, implies a unity 
of nature and imposes a unity on each of 
the fundamental elements of true method. It 
prescribes the right movement from some single 
source, to some single end, by some single way. 
Its function is discharged when it indicates this 
movement and directs it as to such single source, 
end, and way. 

We have found in all knowledge a twofold, a 
subjective and an objective element — a knowing 
and a known. 'A rational method respects the 
change in both aspects. At every stage of prog- 
ress, in all true and right knowledge the corre- 
spondence between these two constituents is main- 
tained perfect and exact. The subjective con- 
stituent increases by the growth effected through 
exercise in a living agent ; and the objective 
constituent increases in exact correspondence ; — 



QUOTATIONS OHi METHOD. 261 

the capacity of knowing is enlarged and intensi- 
fied as the matter known is broadened and deep- 
ened. The view of method, however, will be 
modified according as the one or the other of 
these constituents is prominently regarded. We 
conveniently distinguish, accordingly, a subjec- 
tive and an objective method in knowl- 
edge. . . . 

The subjective method in knowledge respects 
the knowing subject. The source or origin here 
is ever the knowing power or function itself at 
each of the ever advancing stages of its progress. 

The end or goal is primarily the perfection 
of the knowing faculty, and through that the 
perfection, according to its nature, of the whole 
organism of which this faculty is a part ; — a 
goal ever aimed at, but never reached as a final 
knowing, yet in each specific act of knowing 
attained in its own proper degree and measure. 

The way is by a continuous endeavor in ac- 
cordance with the laws of thinking or knowing, in 
which each new measure of thinking energy at- 
tained is made the occasion and means of a still 
more vigorous life of thought. This is prescrib- 
ed by the principle of adjacence ; continuousness 
is but progress from next to next in order of 
proximity or adjacence. .... 

The objective method in knowledge respects 
the matter known. 

The beginning in knowledge here is the datum 
presented to thought. This datum must be of 
the nature of that which can be known ; — must be 
of the nature of truth. Every fresh attainment 
of truth adds so much to the volume of attain- 



262 QUOTATIONS OK METHOD. 

ment which, with what is given on each succes- 
sive occasion of thought, constitutes the datum 
for the succeeding stage. 

The objective end in knowledge is truth ac- 
quired in its complete fulness and comprehensive- 
ness — the universe of truth ; — an end never .fully 
reached, yet in its measure attained in every new 
acquisition. 

The way in objective knowledge is in unde- 
viating course through the adjacent fields of truth, 
from boundary through to boundary, avoiding, as 
far as may be, under the conditions of human 
life, skips and divisions and devious windings. 

9. From Comte's Philomphy of the Sciences^ 
G. H. Lewes, London, 1853. 

Atheists may therefore be regarded as the 
most illogical of theologians, since they attempt 
the theological problems while rejecting the only 
suitable method, (p. 25.) 

That the positive Method is the only Method 
adapted to human capacity, the only one on which 
truth can be found, is easily proved : on it alone 
can prevision of phenomena depend, (p. 39.) 

The present condition of science, therefore, 
exhibits three Methods instead of one : hence the 
anarchy. 

To remedy the evil, all differences must cease : 
one Method must preside, (p. 38.) 

In passing from one science to another, we 
discover the several modifications which method 
(essentially the same in all) undergoes. 

A proper knowledge of the positive method 
can only be acquired in this way. (p. 49.) 

I propose to call the relations of co-existence 



QUOTATIONS OK METHOD. 263 

and succession, usually named Laws, by the 
name of Methods. 

Etymologically, Method is a path leading on- 
wards, a way of transit. The Methods of Na- 
ture would therefore express the paths along 
which the activities of Nature travelled to results 
(phenomena), (p. 55.) 

What we call Laws are nothing but the paths, 
or Methods, along which the Forces (of Nature) 
move. (p. 57.) 

Astronomy is more truly scientific and has at- 
tained the highest degree of philosophical perfec- 
tion that any science can ever pretend to, as re- 
spects Method, — the exact reduction of all phe- 
nomena, both in kind and in degree, to one gen- 
eral law (solar astronomy), (p. 83.) 

A law of Nature can only be discovered by In- 
duction or Deduction. Often, however, neither 
method is of itself sufficient, (p. 105.) 

The Methods in which these masses (suns, 
planets, etc.) move, science attempts to ascer- 
tain ; but in Astronomy we speak of Motion, in 
Chemistry of Combination ; both are Methods of 
the unknown unknowable Force, (p. 113.) 

The methods by which the construction of 
science is promoted are, Methods of Observation, 
Methods of obtaining clear Ideas, and Methods 
of Instruction, (p. 141.) (Whewell.) 

The methods of observation of quantity in 
general are. Numeration, which is precise by the 
nature of number : the Measurement of Space 
and Time, by which aids the Measurement of the 
other ; the Method of Repetition ; the Method 
of Coincidences or Interferences. (p. 145.) 
(Whewell.) 



QUOTATIONS ON SYSTEM. 

APPENDIX B. 

226. From Fleming — Vocabulary of Fhilos- 
opluj, ed. 1867. 

System is a full and connected view of all the 
truths of some department of knowledge. An 
organized body of truth, or truths arrange 
under one and the same idea, which idea is as 
the life or soul which assimilates all those truths. 
No truth is altogether isolated. Every truth 
has relation to some other. And we should 
try to unite the facts of our knowledge so as to 
see them in their several bearings. This we do 
when we frame them into a system. To do so 
legitimately we must begin by analysis and end 
with synthesis. But system applies not only to 
our knowledge, but to the objects of our knowl- 
edge. Thus we speak of the planetary system, 
the muscular system, the nervous system. We 
believe that the order to which we would reduce 
our ideas has a foundation in the nature of 
things. And it is this belief that encourages us 
to reduce our knowledge of things into a system- 
atic order. The doing so is attended with many 
advantages. At the sp.me time a spirit of sys- 
tematizing may be carried too far. It is only in 
so far as it is in accordance with the order of na- 



QUOTATIONS OK SYSTEM. 265 

ture that it can be useful or sound. Condillac 
has a Traite des Systemes, in which he traces 
their causes and their dangerous consequences. 

System, Economy, or Constitution. — "A 
System, Economy, or Constitution, is a one or 
a whole, made up of several parts, but yet that 
the several parts even considered as a whole do 
not complete the idea, unless in the notion of the 
whole you include the relations and respects 
which these parts have to each other. Every 
work, both of nature and of art, is a system ; and 
as every particular thing, both natural and artifi- 
cial, is for some use or purpose out of and beyond 
itself, one may add to what has been already 
brought into the idea of a system, its conducive- 
ness to this one or more ends. Let us instance 
in a watch — suppose the several parts of it taken 
to pieces, and placed apart from each other ; let 
a man have ever so exact a notion of these several 
parts, unless he considers the respects and relations 
which they have to each other, he will not have 
anything like the idea of a watch. Suppose these 
several parts brought together and anyhow united : 
neither will he yet, be the union ever so close, 
have an idea which will bear any resemblance to 
that of a watch. But let him view these several 
parts put together, or consider them as to be put 
together in the manner of a watch ; let him form 
a notion of the relations which these several parts 
have to each other — all conducive in their re- 
spective ways to this purpose, showing the hour 
of the day ; and then he has the idea of a watch. 
Thus it is with resfard to the inward frame of 



2(jQ QUOTATIOi^S Oi^ SYSTEM. 

man. Appetites, passions, affections, and the 
principle of reflection, considered merely as the 
several parts of our inward nature, do not give us 
an idea of the system or constitution of this 
nature ; because the constitution is formed by 
somewhat not yet taken into consideration, 
namely, by the relations which these several 
parts have to each other, the chief of which is 
the authority of reflection or conscience. It is 
from considering the relations which the several 
appetites and passions in the inward frame have 
to each other, and, above all, the supremacy of 
reflection or conscience, that we get the idea of 
the system or constitution of human nature. 
And from the idea itself it will as fully appear, 
that this our nature, i.e., constitution, is adapted 
to virtue, as from the idea of a watch it appears 
that its nature, i.e., constitution or system, is 
adapted to measure time. ' ' 



QUOTATIONS ON ANALYSIS. 

APPENDIX C. 

227. From Fleming's Vocabulary of Philos- 
ophy, ed. 1867. 

Analysis and Synthesis, or decomposition and 
recomposition. Objects of sense and of thought 
are presented to us in a complex state, but we can 
only, or at least best, understand what is simple. 
Among the varied objects of a landscape, I be- 
hold a tree, I separate it from the other objects, 
I examine separately its different parts — trunk, 
branches, leaves, etc., and then reuniting them 
into one whole I form a notion of the tree. The 
first part of this process is analysis, the second 
is synthesis. If this must be done with an indi- 
vidual, it is more necessary with the infinitude 
of objects which surround us, to evolve the one 
out of many, to recall the multitude to unity. 
We compare objects with one another to see 
wherein they agree ; we next, by a synthetical 
process, infer a general law, or generalize the co- 
incident qualities, and perform an act of induction 
which is purely a synthetical process, though 
commonly called analytical. Thus, from our ex- 
perience that bodies attract within certain limits, 
we infer that all bodies gravitate towards each 
other. The antecedent here only says that cer- 



268 QUOTATIONS ON ANALYSIS. 

tain bodies gravitate, the consequent says all bod- 
ies gravitate. They are brought together by the 
mental insertion of a third proposition, which is, 
' ' that nature is uniform. ' ' This is not the 
product of induction, but antecedent to all in- 
duction. The statement fully expressed is, this 
and that body, which we know, gravitate, but 
nature is uniform ; this and that body repre- 
sent all bodies — all bodies gravitate. It is the 
mind which connects these tilings, and the pro- 
cess is synthetical. This is the one universal 
method in all philosophy, and different schools 
have differed only in the way of employing it. 
Method is the following of one thing through 
another. Order is the following of one thing 
after another. Analysis is real, as when a 
chemist separates two substances. Logical, as 
when we consider the properties of the sides and 
angles of a triangle separately, though we can- 
not think of a triangle without sides and angles. 

The instruments of analysis are observation 
and experiment ; of synthesis, definition and 
classification. 

Take down a watch, analysis ; put it up, syn- 
thesis. 

Analysis is decomposing what is compound to 
detect its elements. Objects may be compound, 
as consisting of several distinct parts united, or 
of several properties equally distinct. In the 
former view, analysis will divide the object into 
its parts, and present them to us successively, and 
then the relations by which they are united. In 
the second case, analysis will separate the dis- 



QUOTATIONS Oiq- ANALYSIS. 269 

tinct properties, and sliow the relations of every 
kind which may be between them. 

Analysis is the resolving into its constituent 
elements of a compound heterogeneous substance. 
Thus, water can be analyzed into oxygen and hy- 
drogen, atmospheric air into these and azote. 

Abstraction is analysis, since it is decomposi- 
tion, but what distinguishes it is that it is exer- 
cised upon qualities which by themselves have 
no real existence. Classification is synthesis. 
Induction rests upon analysis. Deduction is 
a synthetical process. Demonstration includes 
both. 



QUOTATIONS ON SYNTHESIS. 

APPENDIX D. 

228. From Fleming's Vocabulary of PJd- 
losophy, ed. 1867. 

Synthesis " consists in assuming the causes 
discovered and established as principles, and by 
them explaining the phenomena proceeding from 
them and proving the explanation. ' ' 

'' Every synthesis which has not started with 
a complete analysis ends at a result which, in 
Greek, is called hypothesis ; instead of which, if 
synthesis has been preceded by a sufficient 
analysis, the synthesis founded upon that anal- 
ysis leads to a result which in Greek is called 
system. The legitimacy of every synthesis is 
directly owing to the exactness of analysis; 
every system which is merely an hypothesis is a 
vain system ; every synthesis which has not been 
preceded by analysis is a pure imagination : but 
at the same time every analysis which does not 
aspire to a synthesis which may be equal to it, 
is an analysis which halts on the way. On the 
one hand, synthesis without analysis gives a false 
science ; on the other hand, analysis without 
synthesis gives an incomplete science. An in- 
complete science is a hundred times more valu- 



QUOTATIONS ON" SYNTHESIS. 271 

able than a false science ; but neither a false 
science nor an incomplete science is the ideal of 
science. The ideal of science, the ideal of phi- 
losophy, can be realized only by a method which 
combines the two processes of analysis and 
synthesis." 



QUOTx\TIONS OX DEFINITION. 

APPENDIX E. 

229. From Fleming's Vocahidary of Fhilos- 
opluj, ed. 1867. 

Definition (definio, to mark out limits). 

'* The simplest and most correct notion of a 
definition is, a proposition declaratory of the 
meaning of a word." 

Definition signifies " laying down a bound- 
ary ;" and is used in Logic to signify " an ex- 
pression which explains any term so as to sepa- 
rate it from everything else, as a boundary sep- 
arates fields. Logicians distinguish definitions 
into Nominal and Real. 

" Definitions are called nominal, which ex- 
plain merely the meaning of the term ; and real, 
which explain the nature of the thing signified 
by that term. Logic is concerned with nominal 
definitions alone. ' ' 

" By a real, in contrast to a verbal or nomi- 
nal definition, the logicians do not intend ' the 
giving an adequate conception of the nature and 
essence of a thing ;' that is, of a thing considered 
in itself, and apart from the conceptions of it 
already possessed. By verbal definition is meant 
the more accurate determination of the significa- 



QUOTATION'S 01^^ DEFINITION". 273 

tion of a word ; by real the more accurate deter- 
mination of the contents of a notion. The one 
clears up the relation of words to notions ; the 
other of notions to things. The substitution of 
notional for real would, perhaps, remove the 
ambiguity. But if we retain the term real, the 
aim of a verbal definition being to specify the 
thought denoted by the word, such definition 
ought to be called notional, on the principle on 
which the definition of a notion is called real ; 
for this definition is the exposition of what things 
are comprehended in a thought." 

" In the sense in which nominal and real 
definitions were distinguished by the scholastic 
logicians, logic is concerned with real, i.e.^ 
notional definitions only ; to explain the mean- 
ing of words belongs to dictionaries or gram- 
mars. ' ' 

' ' There is a real distinction between definitions 
of names and what are erroneously called defini- 
tions of things ; but it is that the latter, along 
with the meaning of a name, covertly asserts a 
matter of fact. This covert assertion is not a 
definition, but a postulate. The definition is a 
mere identical proposition, which gives informa- 
tion only about the use of language, and from 
which no conclusions respecting matters of fact 
can possibly be drawn. The accompanying pos- 
tulate, on the other hand, affirms a fact which 
may lead to consequences of every degTee of im- 
portance. It aflfirms the real existence of things, 
possessing the combination of attributes set forth 
in the definition, and this, if true, may be f oun- 



274 QUOTATIONS OK DEFINITIOiq-. 

dation sufficient to build a whole fabric of scien- 
tific truth." 

Real definitions are divided into essential and 
accidental. An essential definition states what 
are regarded as the constituent parts of the es- 
sence of that which is to be defined ; and an ac- 
cidental definition (or description) lays down 
what are regarded as circumstances belonging to 
it, viz., properties or accidents, such as causes, 
effects, <fcc. 

" Essential definition is divided into physical 
(natural) and logical (metaphysical) ; the phy- 
sical definition being made by an enumeration of 
such parts as are actually separable ; such as are 
the hull, masts, &c. , of a ' ship ' ; the root, trunk, 
branches, bark, &c., of a 'tree.' The logical 
definition consists of the genus and difference, 
which are called by some the metaphysical 
(ideal) parts ; as being not two real parts into 
which an individual object can (as in the former 
case), be actually divided, but only different 
views taken (notions formed) of a class of objects, 
by one mind. Thus a magnet would be defined 
logically, ' an iron ore having attraction for 
iron.'" 

Accidental or descriptive definition may be — 
1 . Causal ; as when man is defined as made 
after the image of God, and for his glory. 2. 
Accidental ; as when he is defined to be ani- 
mal, bipes implume. 3. Genetic ; as when the 
means by which it is made are indicated ; as, if a 
straight line fixed at one end be drawn round by 
the other end so as to return to itself, a circle 



QUOTATION'S OIT DEFIKITIOi;r. 275 

will be described. Or, 4. Per oppositum ; as, 
when virtue is said to be flying from vice. 

The rules of a good definition are : — 1. That it 
be adequate. If it be too narrow, you explain 
a part instead of a whole ; if too extensive, a 
whole instead of a part. 2. That it be clearer 
{i.e., consist of ideas less complex) than the 
thing defined. 3. That it be in just a sufficient 
number of proper words. Metaphorical words 
are excluded because they are indefinite. 

2. From Mill's System of Logic, ^^. 105-106, 
8° edition. 

The simplest and most correct notion of a 
Definition is, a proposition declaratory of the 
meaning of a word ; namely, either the meaning 
which it bears in common acceptation, or that 
which the speaker or writer, for the particular 
purposes of his discourse, intends to annex to it. 
.... This form of definition is the most pre- 
cise and least equivocal of any ; but it is not 
brief enough, and is besides too technical for 
common discourse. The more usual mode of de- 
claring the connotation of a name, is to predicate 
of it another name or names of known significa- 
tion, which connote the same aggregation of at- 
tributes The definition of a name, ac- 
cording to this view of it, is the sum total of all 
the essential propositions which can be framed 
with that name for their subject. All proposi- 
tions the truth of which is implied in the name, 
all those which we are made aware of by merely 
hearing the name, are included in the definition, 
if complete, and may be evolved from it without 



276 QuoTATioj;rs oi^ defikitiok. 

the aid of any other premises ; whether the defi- 
nition expresses them in two or three words,' or 
in a larger number. It is, therefore, not with- 
out reason that Condillac and other writers have 
affirmed a definition to be an analysis. To re- 
solve any complex whole into the elements of 
which it is compounded, is the meaning of anal- 
ysis : and this we do when we replace one word 
which connotes a set of attributes collectively, by 
two or more which connote the same attributes 
singly, or in smaller groups. 



QUOTATIONS ON ABSTRACTION. 

APPENDIX F. 

230. From Fleming's Vocabulary of Philos- 
ophy. 

Abstract, Abstraction (abstractio, from 
abs traho, to draw away from. It is also called 
separatio and resolutio). Dobrisch observes that 
the term abstraction is used sometimes in a psy- 
chological, sometimes in a logical sense. In the 
former we are said to abstract the attention from 
certain distinctive features of objects presented. 
In the latter, we are said to abstract certain por- 
tions of a given concept from the remainder. 
(Mansel.) 

"Abstraction (Psychological)," says Mr. 
Stewart, " is the power of considering certain 
qualities or attributes of an object apart from the 
rest ; or, as I would rathgr choose to define it, 
the power which the understanding has of sepa- 
rating the combinations which are presented to 
it." Perhaps it may be more correctly regarded 
as a process rather than a power — as a function 
rather than a faculty. Dr. Reid has called it " an 
operation of the understanding." . . . The 
chemist separates into their elements those bodies 
which are submitted to his analysis. The psy- 



278 QUOTATIOi^S Oiq" abstractioi^. 

chologist does the same thing mentally. ... In 
contemplating mind, he may think of its capacity 
of feeling without thinking of its power of activ- 
ity, or the faculty of memory apart from any or 
all of the other faculties with which it is al- 
lied. 

Abstraction (Logical), " As we have de- 
scribed it," says Mr. Thomson [Outline of the 
Laws of Thought p. 107), " would include three 
separate acts ; first, an act of comparison, which 
brings several intuitions together ; next, one of 
reflection, which seeks for some marks which 
they all possess, and by which they may be com- 
bined into one group ; and last, one of general- 
ization, which forms the new general notion or 
conception. Kant, however, confines the name 
of abstraction to the last of the three ; others 
apply it to the second. It is not of much conse- 
quence whether we enlarge or narrow the mean- 
ing of the word, so long as we see the various 
steps in the process. The word means a draw- 
ing away of the common marks from all the dis- 
tinctive marks which the single objects have. " . . 
Mr. J. S. Mill uses the term abstract as opposed 
to concrete. By an abstract name he means the 
name of an attribute — by a concrete name the 
name of an object. 



QUOTATIONS ON GENERALIZATION. 

APPENDIX G. 

231. 1. From Fleming's Vocabulary of Phi- 
losophy, ed. 186Y. 

Generalization ' ' is the act of comprehending, 
under a common name, several objects agreeing 
in some point which we abstract from each of 
them, and which that common name serves to in- 
dicate." 

" When we are contemplating several individ- 
uals which resemble each other in some part of 
their nature, we can (by attending to that part 
alone, and not to those points wherein they 
differ) assign them one common name, which will 
express or stand for them merely as far as they 
all agree ; and which, of course, will be appli- 
cable to all or any of them (which process is 
called generalization) ; and each of these names 
is called a common term, from its belonging to 
them all alike ; or a predicable, because it may 
be predicated affirmatively of them or any of 
them." 

Generalization is of two kinds — classification 
and generalization properly so called. 

When we observe facts accompanied by di- 
verse circumstances, and reduce these circum- 



280 QUOTATIONS OK GENERALIZATIOK. 

stances to such as are essential and common, we 
obtain a law. 

When we observe individual objects and ar- 
range them according to their common charac- 
ters, we obtain a class. When the characters 
selected are such as belong essentially to the na- 
ture of the objects, the class corresponds with 
the law. When the character selected is not 
natural the classiiication is artificial. If we were 
to class animals into white and red, we would 
have a classification which had no reference to 
the laws of their nature. But if we classify them 
as vertebrate or invertebrate, we have a classi- 
fication founded on their organization. Artificial 
classification is of no value in science, it is a 
mere aid to the memory. Natural classification 
is the foundation of all science. This is some- 
times called generalization. It is more properly 
classification. 

The law of gravitation is exemplified in the fall 
of a single stone to the ground. But many stones 
and other heavy bodies must have been observed 
to fall before the fact was generalized, and the 
law stated. And in this process of generalizing 
there is involved a principle which experience 
does not furnish. Experience, how extensive 
soever it may be, can only give the particular, yet 
from the particular we rise to the general, and 
affirm not only that all heavy bodies which have 
been observed, but that all heavy bodies whether 
they have been observed or not, gravitate. In 
this is implied a belief that there is order in na- 
ture, that under the same circumstances the same 



QUOTATIONS OK GENERALIZATIOK. 281 

substances will present the same plienomena. 
This is a principle furnished by reason, the pro- 
cess founded on it embodies elements furnished 
by experience. 

The results of generalization are general no- 
tions expressed by general terms. Objects are 
classed according to certain properties which they 
have in common, into genera and species. 
Hence arose the question which caused centuries 
of acrimonious discussion. Have genera and 
species a real, independent existence, or are they 
only to be found in the mind ? 

The principle of generalization is, that be- 
ings howsoever different agree or are homo- 
geneous in some respect. 

2. From Jevon's Principles of Science, pp. 
597-599, ed. 1877. 

The term generalization, as commonly used, 
includes two processes which are of different 
character, but are often closely associated to- 
gether. In the first place, we generalize when 
w^e recognize even in two objects a common na- 
ture. We cannot detect the slightest similarity 
without opening the way to inference from one 
case to the other. If we compare a cubical crys- 
tal with a regular octahedron, there is little ap- 
parent similarity ; but, as soon as we perceive that 
either can be produced by the symmetrical modi- 
fication of the other, we discover a groundwork of 
similarity in the crystals, which enable us to infer 
many things of one, because they are true of the 
other. Our knowledge of ozone took its rise 
from the time when the similarity of smell, at- 



282 QUOTATIOi^S OK GEIS"EKALIZATIOK. 

tending electric sparks, strokes of liglitning, and 
the slow combustion of pliosphorus, was noticed 
by Schonbein. There was a time when the rain- 
bow was an inexplicable phenomenon — a portent, 
like a comet, and a cause of superstitious hopes 
and fears. But we find the true spirit of science 
in Roger Bacon, who desires us to consider the 
objects which present the same colours as the rain- 
bow ; he mentions hexagonal crystals from Ire- 
land and India, but he bids us not suppose that 
the hexagonal form is essential, for similar colours 
may be detected in many transparent stones. 
Drops of water scattered by the oar in the sun, 
the spray from a water-wheel, the dewdrops lying 
on the grass in the summer morning, all display 
a similar phenomenon. No sooner have Ave 
grouped together these apparently diverse in- 
stances, than we have begun to generalise, and 
have acquired a power of applying to one in- 
stance what we can detect of others. Even when 
we do not apply the knowledge gained to new 
objects, our comprehension of those already ob- 
served is greatly strengthened and deepened by 
learning to view them as particular cases of a 
more general property. 

A second process, to which the name of gen- 
eralization is often given, consists in passing from 
a fact or partial law to a multitude of unexamined 
cases, which we believe to be subject to the same 
conditions. Instead of merely recognising sim- 
ilarity as it is brought before us, we predict its 
existence before our senses can detect it, so that 
generalisation of this kind endows us with a 



QUOTATIONS 01^ GEiq-ERALIZATIOi^. 283 

prophetic power of more or less probability. 
Having observ^ed that many substances assume, 
like water and mercury, the three states of solid, 
liquid, and gas, and having assured ourselves by 
frequent trial that the greater the means we 
possess of heating and cooling, the more sub- 
stances we can vaporise and freeze, we pass con- 
fidently in advance of fact, and assume that all 
substances are capable of these three forms. 
Such a generalisation was accepted by Lavoisier 
and Laplace before many of the corroborative 
facts now in our possession were known. The 
reduction of a single comet beneath the sway of 
gravity was considered sufficient indication that 
all comets obey the same power. Few persons 
doubted that the law of gravity extended over 
the whole heavens ; certainly the fact that a few 
stars out of many millions manifest the action of 
gravity, is now held to be sufficient evidence of 
its general extension over the visible universe. 



QTJOTATIOXS ON CLASSIFICATIOX. 

APPENDIX H. 

232. 1. From Ylemmg^ & Vocabulari/ of Phl- 
loHophij, ed. 1858, pp. 91-92. 

" Montesquieu observed very justly, that in 
their classification of the citizens, tlie great 
legislators of antiquity made the greatest display 
of their powers, and even soared above them- 
selves." Burke, On the French Revolution. 

" A class consists of several things coming 
under a common description. ' ' Whately, Log. , 
b. i., § 3. 

" The sortinsj of a multitude of things into 
parcels, for the sake of knowing them better, 
and remembering them more easily, is classifica- 
tion. When we attempt to classify a multitude 
of things, we first observe some respects in 
which they differ from each other ; for we could 
not classify things that are entirely alike ; as, 
for instance, a bushel of peas ; Ave then separate 
things that are not alike, and bring together 
things that are similar." Taylor, Elements of 
Thought. 

" In every act of classification, two steps must 
be taken ; certain marks are to be selected, the 
possession of which is to be the title to admis- 



QUOTATIONS OH CLASSIFICATION. 285 

sion into the class, and then all the objects that 
possess them are to be ascertained. When the 
marks selected are really important and con- 
nected closely with the nature and functions of 
the thinir, the classification is said to be natu- 
ral ; where they are such as do not affect the 
nature of the objects materially, and belong in 
common to things the most different in their 
main properties, it is artificial" Thomson, 
Outline of Laws of Thought, 2d edit., p. 377. 

The condition common to both modes of clas- 
sification, is to comprehend ev^erything and to 
suppose nothing. But the rules for a natural 
classification are more strict than for an artificial 
or arbitrary one. We may classify objects arbi- 
trarily in any point of view in which we are 
pleased to regard them. But a natural classifi- 
cation can only proceed according to the real 
nature and qualities of the objects. The advan- 
tages of classification are to give a convenient 
form to our acquirements, and to enlarge our 
knowledge of the relations in which different ob- 
jects stand to one another. A good classifica- 
tion should — 1st, Rest on one principle or analo- 
gous principles. 2d, The principle or princi- 
ples should be of a constant and permanent char- 
acter. 3d, It should be natural, that is, even 
when artificial, it should not be violent or 
forced. 4th, It should clearly and easily apply 
to all the objects classified. 

The principles on which classification rests 
are these: — 1st, of Generalization; 2d, of 
Specification ; and 3d, of Continuity. 



286 QUOTATION'S OIT CLASSIFICATIOIT. 

Classification proceeds upon observed resem- 
blances. Generalization rests upon the princi- 
ple, that the same or similar causes will produce 
similar effects. — Mill, Log,, b. i., chap. 7, § 4 ; 
McCosh, Typical Forms, b. iii., chap. 1. 

2. From Jevons' Elementary Lessons iyi Logic, 
ed. 1878, pp. 276-286. 

It may be said that the subject we are treating 
is coextensive with the science of logic. All 
thought, all reasoning, so far as it deals with 
general names or ge; eral notions, may be said 
to consist in classification. Every common 
name or general name is the name of a class, and 
every name of a class is a common name. 
" Metal " is the name of one class of substantives 
so often used in our syllogistic examples ; 
" Element" of another class, of which the former 
class is part. Reasoning has been plausibly rep- 
resented to consist in afiirming of the parts of a 
class whatever may be aflirmed of the whole. 
Every law of nature which we arrive at enables 
us to classify together a number of facts, and it 
would hardly be too much to define logic as the 
theory of classification. . . . Classification 
may perhaps be best defined as the arrange- 
ment of things, or our notions of them, accord- 
ing to their resemblances, or identities. 

Every class should so be constituted as to con- 
tain objects exactly resembling each other in 
certain definite qualities, which are stated in the 
definition of the class. The more numerous and 
extensive the resemblances which are thus indi- 



QUOTATIOI^S OK CLASSIFICATION. 287 

cated by any system of classes, the more perfect 
and useful must that system be considered. 

Mr. Mill thus describes his view of the mean- 
ing — " Classification is a contrivance for the best 
possible ordering of the ideas of objects in our 
minds ; for causing the ideas to accompany or 
succeed one another in such a way as shall give 
us the greatest command over our knowledge 
already acquired, and lead most directly to the 
acquisition of more. The general problem of 
classification, in reference to these purposes may 
be stated as follows : To provide that things shall 
be thought of in such groups, and those groups 
in such an order, as will best conduce to the re- 
membrance, and to the ascertainment of their 
laws. ' ' 

A collection of objects may be classified in an 
indefinite number of ways. Any quality which 
is possessed by some and not by others may be 
taken as the first difference, and the groups thus 
distinguished may be subdivided in succession by 
any other qualities taken at will. Thus a library 
of books might be arranged, (1) according to 
size, (2) according to the language in w-hich 
they are written, (3) according to the alphabetic 
order of their authors' names, (4) according 
to their subjects ; and in various other ways. 
In large libraries and in catalogues such modes 
of arrangement are adopted and variously com- 
bined. . . . The population of a kingdom, again, 
may be classified in an almost endless number of 
wiiys with regard to different purposes or sci- 
ences. The population of the United Kingdom 



288 QUOTATIONS OK CLASSIFICATIOiq'. 

may be divided according to their place of birth, 
as Eng'Hsh, Welsh, Scotch, Irish, Colonial-born 
and aliens. The ethnographer would divide 
them into Anglo-Saxons, Cymri, Gaels, Picts, 
&c. The statist arranges them according to age ; 
to condition, as married, unmarried, widowed, 
etc. ; to state of body, as able, incapacitated, 
blind, imbecile. 

In the natural world, again, we may make va- 
rious classifications. Plants may be arranged 
according to the country from which they are 
derived ; the kind of place or habitat in which 
they flourish ; the time they live, as annual, 
biennial, perennial ; their size, as herbs, shrubs, 
trees ; their properties, as esculents, drugs, or 
poisons : all these are distinct from the classifi- 
cations which the botanist devises to represent 
the natural affinities or relationships of plants. 
It is thus evident that in making a classification 
we have no one fixed method which can be ascer- 
tained by rule, but that an indefinite number of 
choices or alternatives are usually open to us. 
Logic cannot in such cases do much ; and it is 
really the work of the special sciences to investi- 
gate the character of the classification required. 
AH that logic can do is to point out certain gen- 
eral requirements and principles. 

The first requisite of a good classification is, 
that it should be appropriate to the purpose in 
hand; that is to say, the points of resemblance 
selected to form the leading classes shall be those 
of importance to the practical use of the classifi- 
cation. All those things must be arranged to- 



QUOTATIONS OK CLASSIFICATIOK. 289 

gether which require to be treated alike, and 
those things must be separated Avhich require to 
be treated separately. 

Another and, in a scientific point of view, 
the most important requisite of a good classifica- 
tion, is that it shall enable the greatest possi- 
ble number of general assertions to be made. 
This is the criterion, as stated by Dr. Whewell, 
which distinguishes a natural from an artificial 
system of classification, and we must carefully 
dwell upon its meaning. It will be apparent 
that a good classification is more than a mere 
orderly arrangement ; it involves a process of 
induction which will bring to light all the more 
general relations which exist between the things 
classified. An arrangement of books will gen- 
erally be artificial ; the octavo volumes will not 
have any common character except being of an 
octavo size. An alphabetical arrangement of 
names again is exceedingly appropriate and con- 
venient to many purposes, but is artificial because 
it allows of few or no general assertions. We 
cannot make any general assertions whatever 
about persons because their names happen to 
begin with an A or a B, a P or a W. 

In a classification of plants again we meet 
with most deep and natural distinctions between 
the great classes called Exogens, Endogens, and 
Acrogens. . . . These are the very widest 
classes in what is called the natural system of 
botanical arrangement; but similar principles 
are observed in all its minor classes. 

The continual efforts of botanists are directed 



290 QUOTATIONS OK CLASSIFICATION". 

to bringing tlie great multitudes of plants to- 
gether in species, genera, orders, classes, and in 
various intermediate groups, so that the members 
of each group shall have the greatest number of 
points of mutual resemblance and the fewest 
points of resemblance to members of other 
groups. Thus is best fulfilled the great purpose 
of classification, which reduces multiplicity to 
unity, and enables us to infer of all the other 
members of a class what we know of any one 
member, provided we distinguish properly be- 
tween those qualities which are likely or are 
known to belong to the class, and those which 
are peculiar to the individual. It is a necessary 
condition of correct classification, as remarked by 
Prof. Huxley, that the definition of a group 
shall hold exactly true of all the members of a 
group, and not of the members of any other 
group. . . . 

Natural classifications give us the deepest re- 
semblances and relations, and may lead us ulti- 
mately to a knowledge of the way in which the 
varieties of things are produced. They are, 
therefore, essential to a true science, and may al- 
most be said to constitute the framework of the 
science. 

Closely connected with the process of Classifi- 
cation is that of abstraction. To abstract is to 
separate the qualities common to all individuals 
of a group from the peculiarities of each individ- 
ual. The notion " triangle" is the result of ab- 
straction in so far as we can reason concerning 
triangles, wdthout any regard to the particular 



QUOTATIOInTS ok CLASSIFICATION". 291 

size or shape of any one triangle. All classifica- 
tion implies abstraction, for in framing and 
defining the class I must separate the common 
qualities from the peculiarities. When I ab- 
stract, too, I form a general conception, or one, 
which, generally speaking, embraces many ob- 
jects. If, indeed, the quality abstracted is a pe- 
culiar property of the class, or one which belongs 
to the whole and not to any other objects, I 
may not increase the extent of the notion, so that 
Mr. Herbert Spencer is, perhaps, right in holding 
that we can abstract without generalizing. 
We often use this word generalization, and 
the process may be defined as inferring of a whole 
class what we know only of a part. Whenever 
we regard the qualities of a thing as not confined 
to that thing only but as extended to other ob- 
jects ; when, in fact, w^e consider a thing only 
as a member of a class, we are said to generalize. 
. . . Dr. Whewell added to the superabundance 
of terms to express the same processes when he 
introduced the expression Colligation of facts. 

Whenever two things are found to have simi- 
lar properties so as to be placed in the same 
class they may be said to be connected to- 
gether. 

We connect together the places of a planet as 
it moves round the sun, when we conceive them 
as points upon a common ellipse. Whenever 
we thus join together previously disconnected 
facts, by a suitable general notion or hypothesis, 
we are said to colligate them. Dr. Whewell 



292 QUOTATIOKS Oi^T CLASSIFICATION". 

adds that the general conceptions employed must 
be (1) clear, and (2) appropriate ; but it may 
well be questioned whether there is anything 
really different in these processes from the gen- 
eral process of natural classification which we 
have considered. 



QUOTATIONS ON INDUCTION. 



APPENDIX I. 



233. 1. From Smith — Synonyms Discrimi- 
nated — " Inference"— ed. 1878. 

Inference (Lat. in, and ferre, to bring) is the 
broadest of these terms (see below), denoting any- 
process by which from one truth or fact laid down 
or known we draw another. Inference may be 
either by induction or deduction, and hence may 
be probable or certain. Inference by induction 
is more or less probable, except where all cases 
of the kind have been collated, when it ceases, 
strictly speaking, to be inference, and is only the 
assigning of a common name, or stating an uni- 
versal proposition. From having seen twenty 
swans all white, one might infer that all swans 
are so. This would be only a probability in it- 
self, and, as a fact, not true. In induction we 
observe a sufficient number of individual facts 
or cases, and extending by analogy what is true 
of them to others of the same class, establish a 
general principle or law. This is the method of 
physical science. The process of deduction is 
the converse of this. We lay down a general 
truth, and connect a particular case with it by 
means of a middle term. When inference is 



294 QUOTATIOI^S OK IKDUCTIOl^. 

conducted by the syllogistic process, it is Deduc- 
tion (Lat. deducere, to draw from), which, if 
rightly conducted, must be logically sound, 
though not necessarily true in fact. In a chain 
of reasoning the minor, subordinate, or less 
fully-expressed conclusions are called inferences, 
as distinguished from the great common infer- 
ence or Conclusion, which terminates and estab- 
lishes, or, as it were, shuts up (Concludere, to 
shut) the argument. A conclusion is a proposi- 
tion viewed relatively to others from which it has 
been deduced. A Consequence (Lat. consequi, 
to follow) is a conclusion regarded as admitting 
of degrees of closeness or directness. Betw^een 
the first stage of any argument and any particu- 
lar consequence several links of reasoning may 
intervene. Hence the common phrase, ' ' remote 
consequences," as meaning results which will 
follow sooner or later from what has been stated 
or conceded. 

2. From Day's Elements of Logic, ed. 1868, 
p. 226. 

The accepted characteristics of Induction 
are : 

(«) It is a process of Thought that is identical 
in essential character in all those movements of 
Intelligence which induce, which infer mediately 
otherwise than by deduction. There is but one 
Induction, as there is but one Deduction in all 
Thought. 

(6) It is a reasoning, being a derivative Judg- 
ment, not a Concept ; an inference from a 
datum, implying a new proper Judgment-Cog- 



QUOTATIONS OX li^DUCTIOI^r. 295 

nition, not a mere synthesis of subjects or of 
predicates — that is, not a Concept. 

(c) It is a mediate reasoning, being derived not 
from a single Judgment, but from a phirality of 
Judgments, related to each other under the rela- 
tionship of part to complementary part in two 
of their terms which are alike related to the 
third or middle term as parts to a whole. 

3. From Fleming's Vocabulary of JPhilosophj, 
ed. 1858, pp. 252-254. 

Method or Process of Induction. — " It has 
been said that Aristotle attributed the discovery 
of induction to Socrates, deriving the word 
from the Socratic accumulation of instances, 
serving as antecedents to establish the requisite 
conclusion." — Devey, Log., p. 151, note. 

Induction is a kind of argument which infers, 
respecting a whole class, what has been ascer- 
tained respecting one or more individuals of that 
class. — Whately, Log., book ii., chap. 5, g 5. 

"Induction is that operation of mind by 
which we infer that what we know to be true in 
a particular case or cases, will be true in all cases 
which resemble the former in certain assignable 
respects. In other words, induction is the pro- 
cess by which we conclude that what is true of 
certain individuals of a class, is true of the whole 
class, or that what is true at certain times will be 
true under similar circumstances at all times."- — 
Mill, Log., b. iii., ch. 2, § 1, 

" Induction is usually defined to be the pro- 
cess of drawing a general rule from a sufficient 
number of particular cases ; deduction is the 



296 QUOTATIONS OK IKDUCTIOI?-. 

converse process of proving tliat some property 
belongs to the particular case from the consider- 
ation that it belongs to the whole class in which 
the case is found. That all bodies tend to fall 
towards the earth is a truth which we have ob- 
tained from examining a number of bodies com- 
ing under our notice, by induction ; if from this 
general principle we argue that the stone we 
throw from our hand will show the same ten- 
dency, we adopt the deductive method. . . . 
More exactly, we may define the inductive 
method as the process of discovering laws and 
rules from facts, and causes from effects ; and 
the deductive, as the method of deriving facts 
from laws and effects from their causes." — 
(Thomson, Outline of the Laws of Thought, 2d 
edit., pp, 321, 323.) 

According to Sir William Hamilton [Discus- 
sions, p. 156), "Induction has been employed 
to designate three very different operations — 1. 
The objective process of investigating particular 
facts, as preparatory to induction, which is not 
a process of reasoning of any kind. 2. A ma- 
terial illation of the universal from the singular, 
as warranted either by the general analogy of 
nature, or the special presumptions afforded by 
the object-matter of any real science. 3. A for- 
mal illation of the universal from the individual, 
as legitimated solely by the laws of thought, and 
abstract from the conditions of this or that ' par- 
ticular matter.' The second of these is the in- 
ductive method of Bacon, which proceeds by way 
of rejections and conclusions, so as to arrive at 



QUOTATIOITS OK liTDUCTIOiq". 297 

those axioms or general laws from which we infer 
by way of synthesis other particulars unknown 
to us, and perhaps placed beyond reach of direct 
examination. Aristotle's definition coincides 
with the third, and 'induction is an inference 
drawn from all the particulars ' [Prior Anali/t., 
ii., c. 23). The second and third have been 
confounded. But the second is not a logical pro- 
cess at all, since the conclusion is not necessarily 
inferrible from the premiss, for the some of the 
antecedent does not necessarily legitimate the all 
of the conclusion, notwithstanding that the pro- 
cedure may be warranted by the material problem 
of the science or the fundamental principles of 
the human understanding. The third alone is 
properly an induction of Logic ; for Logic does 
not consider things, but the general forms of 
thought under which the mind conceives them ; 
and the logical inference is not determined by 
any relation of casuality between the premiss 
and the conclusion, but by the subjective relation 
of reason and consequence as involved in the 
thought." 

" The Baconian or Material Induction pro- 
ceeds on the assumption of general laws in the 
relations of physical phenomena, and endeavours, 
by select observations and experiments, to detect 
the law in any particular case. This, whatever 
be its value as a general method of physical in- 
vestigation, has no place in Formal Logic. The 
Aristotelian or Formal Induction proceeds on 
the assumption of general laws of thought, and 
inquires into the instances in which, by such 



298 QUOTATIONS OK IKDUCTIOK. 

laws, we are necessitated to reason from an accu- 
mulation of particular instances to an universal 
rule." — Mansel, Prolegom. Log., p. 209. 

Principle of Induction. — By tlie principle of 
induction is meant the ground or warrant on 
which we conclude that, what has happened in 
certain cases, which have been observed, will also 
happen in other cases, which have not been ob- 
served. This principle is involved in the words 
of the wise man, Eccles. i. 9, " The thing- that 
hath been, it is that which shall be : and that 
which is done is that which shall be done." In 
nature there is nothing insulated. All things 
exist in consequence of a sufficient reason, all 
events occur according to the efficacy of proper 
causes. In the language of Newton, Effectuum 
naturalium ejusdem generis eaedem sunt 
causffi. The same causes produce the same 
effects. The principle of induction is an appli- 
cation of the principle of casuality. Phenomena 
have their proper causes, and these causes ope- 
rate according to a fixed law. This law has been 
expressed by saying, substance is persistent. 
Our belief in the established order of nature is a 
primitive judgment, according to Dr. Reid and 
others, and the ground of all the knowledge we 
derive from experience. According to others 
this belief is a result or inference derived from 
experience. 

4. From AAHie well's Novum Organon Reno- 
vatum, 3d edition, 1858, p. 139 : — 

The Pure Mathematical Sciences can hardly 
be called Inductive Sciences. Their principles 



QUOTATIONS Oiq- IITDUCTIOK. 299 

are not obtained by Induction from Facts, but 
are necessarily assumed in reasoning upon the 
subject-matter which those sciences involve. 

5. From English Cyclopcedia, edition 1867. 

Induction {ETtayoDyjj), as defined by Arch- 
bishop Whately, is " a kind of argument which 
infers respecting a whole class what has been as- 
certained respecting one or more individuals of 
that class. ' ' According to Sir William Hamilton 
the word has been employed to designate three 
very different operations : — 1. The objective pro- 
cess of investigating particular facts, as prepara- 
tory to Induction, which he observes is manifestly 
not a process of reasoning of any kind ; 2. A ma- 
terial illation of a universal from a singular, as 
warranted either by the general analogy of na- 
ture or the special presumptions afforded by the 
object matter of any real science ; 3. A formal 
illation of a universal from the individual, as 
legitimated solely by the laws of thought and 
abstracted from the conditions of any particular 
matter. The second of these operations is the 
inductive method of Bacon, which proceeds by 
means of rejections and conclusions, so as to ar- 
rive at those axioms or general laws from which 
we may infer by way of synthesis other particu- 
lars unknown to us, and perhaps placed beyond 
reach of direct examination. (' Nov. Org.,^ 
' Aph.,^ c. iii., c. v.) Aristotle's definition co- 
incides with the third, and induction " is an in- 
ference drawn from all particulars." (' Prior 
Analy.j^ ii., c. xxiii.) The second and third 
processes are improperly confounded by most 
writers on logic, and treated as one simple and 



300 QUOTATIONS OK IKDUCTIOK. 

purely logical operation. But the second is not 
a logical process at all ; since tlie conclusion is 
not necessarily inferrible from the premise, for 
the some of the antecedent does not necessarily 
legitimate the all of the conclusion, notwithstand- 
ing that the procedure may be warranted by the 
material problem of the science, or the funda- 
mental principles of the human understanding. 
The third alone is properly an induction of logic ; 
for logic does not consider things, but the general 
forms of thought under which the mind conceives 
them ; and the logical inference is not deter- 
mined by any relation of causality between the 
premise and conclusion, but by the subjective 
relation of reason and consequence as involved 
in the thought. The inductive process is exactly 
the reverse of the deductive ; for while the latter 
proceeds from the whole to the part, the former 
ascends from the part to the whole : since it is 
only under the character of a constituted or con- 
taining whole, or as a constituent and contained 
part, that anything can become the term of logi- 
cal argumentation. Of these two processes. Sir 
William Hamilton gives the following figures : — 

Induction. Deduction. 

X Y Z are A. B is A. 

X Y Z are whole B. X Y Z are under B. 

. •. whole B is A. . ♦. X Y Z are A. 

or, or, 

A contains X Y Z. A contains B. 

X Y Z contains B. B contains X Y Z. 

. •. A contains B. . •. A contains X Y Z. 
This confusion of material and logical indue- 



QUOTATIONS 01^ IKDUCTIOK. 301 

tion led Gillies and others to insist on tlie same- 
ness of the Baconian and Aristotelian induction ; 
while Campbell and Dugald Stewart, who totally 
mistook the value of all logical inference, yet 
rightly maintained their difference. 

By Aristotle, induction and deduction are 
viewed as in certain respects similar in form ; 
but in others as diametrically opposed, the latter 
being an analysis of the whole into its parts, by 
descending from the more general to the more 
particular ; but the former descends by a syn- 
thetical process from the parts to the whole. 
The logicians, who misapprehended the nature of 
induction, reduced it to a deductive syllogism of 
the third form, and thereby overthrew the valid- 
ity of all deduction itself, since the latter is only 
possible by means of the former, which legiti- 
mates the proposition from which its reasoning 
proceeds. 

Again, the Aristotelian induction was drawn 
from all the particulars, whereas the confusion 
which Sir W. Hamilton has pointed out gave 
rise to a division of the inductive process into 
perfect and imperfect, according as the enumera- 
tion of particulars is complete or incomplete. 
The latter gives only a probable result, whereas 
the necessity of the conclusion is essential to all 
logical inference, as its demonstrative stringency 
depends upon the form of the illation, and not 
upon the truth of the premises. It is proper to 
add, that no one ever knew the distinction be- 
tween the imperfect and perfect forms of the 
conclusion better than Aristotle himself. 



302 quotatio:n^s ok in^ductiois*. 

Induction (Mathematics). The method of 
induction, in the sense in which the word is used 
in natural philosophy, is not known in pure 
mathematics. There certainly are instances in 
which a general proposition is proved by a col- 
lection of the demonstrations of different cases, 
which may remind the investigator of the induc- 
tive process, or the collection of the general from 
the particular. Such instances however must 
not be taken as permanent, for it usually happens 
that a general demonstration is discovered as 
soon as attention is turned to the subject. 

There is however one particular method of 
proceeding which is extremely common in math- 
ematical reasoning, and to which we propose to 
give the name of successive induction. It has 
the character of induction as defined by the logi- 
cians, because it is really the collection of a gen- 
eral truth from a demonstration which implies 
the examination of every particular case ; but it 
adds to the necessary character of induction that 
each case depends upon one or more of those 
which precede. Substituting demonstration for 
observation, the mathematical process is truly 
inductive. A couple of instances of the method 
will enable the mathematical reader to recognize 
a mode of investigation with which he is already 
familiar. 

Example 1. — The sum of any number of suc- 
cessive odd numbers, beginning from unity, is a 
square number, namely, the square of half the 
even number which follows the last odd number. 



QUOTATIONS OK IKDUCTIOK. 303 

Let this proposition be true in any one single in- 
stance ; that is, n being some whole number, let 
1, 3, 5 .... up to 211 + 1 put together give 
(n + l)^ Then the next odd number being 
2n + 3, the sum of all the odd numbers up to 
2n + 3 will be (n+l)' + 2 n + 3, or ii'+4ii+4, 
or (n-\-2f. But n-1-2 is the half of the even 
number next following 2n+3 : consequently, 
if the proposition be true of any one set of odd 
numbers, it is true of one more. But it is true 
of the first odd number 1, for this is the square 
of half the even number next following. Conse- 
quently, being true of 1, it is true of 1+3 ; be- 
ing true of 1+3, it is true of 1+3+5 ; being 
true of 1+3+5, it is true of 1+3+5+7, and 
so on ad iniiiiitum. 

Example 2. — The formula X" — 4\ n being a 
whole number, is always algebraically divisible 
by X — a. 

xn _ a^ = X" — a"-ix+ a^-'x — a" 

r=x(x"-^— a"-i)+a'^-^ (x— a) 
In this last expression the second term a """^ 
/x— a) is obviously divisible by x— a: if then 
any one of the succession 

x-a, x^-a^x^-a^ x^-aS &c. 
be divisible by x— a, so is the next. But this is 
obviously true of the first, therefore it is true of 
the second ; being true of the second, it is true 
of the third ; and so on, ad infinitum. 

There are cases in which the successive induc- 
tion only brings any term within the general rule, 
when two, thr^e, or more of the terms immedi- 
ately preceding are brought within it. Thus 



304 QUOTATIONS OK II^DUCTIOIS". 

in the application of tliis method to tlie deduc- 
tion of the well known consequence of 

X -\ — = 2 COS. 0, 

X 

namely, 

x^ -\ = 2 COS. n B, 

x"" 

it can only be shown that any one case of this 
theorem is true, by showing that the preceding 
two cases are true ; thus its truth, when n = 5 
and n = 6, makes it necessarily follow when 
n = 7. In this case the two first instances must 
be established (when n=:l by hypothesis, and 
when n=:2 by independent demonstration), 
which two establish the third, the second and 
third establish the fourth, and so on. 

An instance of mathematical induction occurs 
in many equations of differences, in every recur- 
ring series, etc. 

6. From Jevons' Elementary Lessons in Logic, 
pp. 208-28, ed. 1878. 

To express the difference between knowledge 
derived deductively and that obtained induct- 
ively the Latin phrases d 2^^^ori and d pos- 
teriori are often used. By A priori reason- 
ing we mean argument based on truths pre- 
viously known ; A posteriori reasoning, on 
the contrary, proceeds to infer from the conse- 
quences of a general truth what that gen- 
eral truth is. Many philosophers consider that 
the mind is naturally in possession of certain 



QUOTATIONS OK IKDUCTION". 305 

laws or truths wliicli it must recognise in every 
act of thought ; all such, if they exist, would be 
d priori truths. It cannot be doubted, for in- 
stance, that we must always recognise in thought 
the three Primary Laws of Thought considered 
in Lesson xiv. We have there an d priori 
knowledge that " matter cannot both have weight 
and be without weight," or that " every thing 
must be either self-luminous or not self-lumin- 
ous. ' ' But there is no law of thought which 
can oblige us to think that matter has weight, 
and luminous ether has not weight ; that Jupiter 
and Venus are not self-luminous, but that comets 
are to some extent self-luminous. These are 
facts which are no doubt necessary consequences 
of the laws of nature and the general constitution 
of the world ; but as we are not naturally ac- 
quainted with all the secrets of creation, we 
have to learn them by observation, or by the d 
posteriori method. 

It is not however usual at the present time 
to restrict the name d priori to truths obtained 
altogether without recourse to observation. 
Knowledge may originally be of an d posteriori 
origin, and yet having been long in possession, 
and having acquired the greatest certainty, it 
may be the ground of deductions, and may then 
be said to give d priori knowledge. Thus it is 
now believed by all scientific men that force 
cannot be created or destroyed by any of the 
processes of nature. If this be true the force 
which disappears when a bullet strikes a target 
must be converted into something else, and on 



306 QUOTATIONS OK INDUCTIOiq-. 

d priori grounds we may assert tliat heat will be 
the result. It is true that we might easily learn 
the same truth d posteriori, by picking up por- 
tions of a bullet which has just struck a target 
and observing that they are warm. But there 
is a great advantage in d pi'iori knowledge ; we 
can often apply it in cases where experiment or 
observation would be difficult. If I lift a stone 
and then drop it, the most delicate instruments 
could hardly show that the stone was heated by 
striking the earth ; yet on d priori grounds I 
know that it must have been so, and can easily 
calculate the amount of heat produced. Simi- 
larly we know, without the trouble of observa- 
tion, that the Falls of Niagara and all other 
waterfalls produce heat. This is fairly an in- 
stance of d priori knowledge because no one 
that I have heard of has tried the fact or proved 
it d post€rio7'i ; nevertheless the knowledge is 
originally founded on the experiments of Mr. 
Joule, who observed in certain well-chosen cases 
how much force is equivalent to a certain amount 
of heat. The reader, however, should take care 
not to confuse the meaning of d priori thus ex- 
plained with that given to the words by the phi- 
losophers who hold the mind to be in the pos- 
session of knowledge indepeodently of all obser- 
vation. 

It is not difficult to see that the d priori 
method is equivalent to the synthetic method 
considered in intension, the d posteriori method 
of course being equivalent to the analytic 
method. But the same difference is really ex- 



QUOTATIONS ON INDUCTION. 307 

pressed in the words deductive and inductive ; 
and we shall frequently need to consider it in 
the following lessons. 

PERFECT INDUCTION AND THE INDUCTIVE 
SYLLOGISM. 

We have in previous lessons considered de- 
ductive reasoning, which consists in combining 
two or more general propositions synthetically, 
and thus arriving at a conclusion which is a 
proposition or truth of less generality than the 
premises, that is to say, it applies to fewer indi- 
vidual instances than the separate premises from 
which it was inferred. When I combine the 
general truth that " metals are good conductors 
of heat," with the truth that " aluminium is a 
metal," I am enabled by a syllogism in the mood 
Barbara to infer that '' aluminium is a good con- 
ductor of heat." As this is a proposition con- 
cerning one metal only, it is evidently less gen- 
eral than the premise, which referred to all 
metals whatsoever. In induction, on the con- 
trary, we proceed from less general, or even from 
individual facts, to more general propositions, 
truths, or, as we shall often call them. Laws of 
Nature. When it is known that Mercury moves 
in an elliptic orbit round the Sun, as also Venus, 
the Earth, Mars, Jupiter, &c,, we are able to 
arrive at the simple and general truth that " all 
the planets move in elliptic orbits round the 
sun. ' ' This is an example of an inductive pro- 
cess of reasoning. 

It is true that we may reason without ren- 



308 QUOTATIOl^S OIT INDUCTION". 

dering our conclusion either more or less general 
than the premises, as in the following : — 
Snowdon is the hig^hest mountain in Enofland or 

Wales. 
Snowdon is not so high as Ben Nevis. 
Therefore the highest mountain in England or 

Wales is not so high as Ben Nevis. 
Again : 

Lithium is the lightest metal known. 
Lithium is the metal indicated hy one bright red 

line in the spectrum.* 
Therefore the lightest metal known is the metal 

indicated by a spectrum of one bright red line. 

In these examples all the propositions are 
singular propositions, and merely assert the iden- 
tity of singular terms, so that there is no altera- 
tion of generality. Each conclusion applies to 
just such an object as each of the premises applies 
to. To this kind of reasoning the apt name of 
Traduction has been given. 

Induction is a much more difficult and more 
important kind of reasoning process than Tra- 
duction or even Deduction ; for it is engaged in 
detecting the general laws or uniformities, the 
relations of cause and effect, or in short all the 
general truths that may be asserted concerning 
the numberless and very diverse events that take 
place in the natural world around us. The 
greater part, if not, as some philosophers think, 
the whole of our knowledge, is ultimately due to 
inductive reasoning. The mind, it is plausibly 

* Roscoe's Lessons in E<,ementary Chemistry, p. 199. 



QUOTATIONS OK INDUCTIOiq'. 309 

said, is not furnished with knowledge in the 
form of general propositions ready made and 
stamped upon it, but is endowed with powers of 
observation, comparison, and reasoning, which 
are adequate, when Avell educated and exercised, 
to procure knowledge of the world without us 
and the worl i within the human mind. Even 
when we argue synthetically and deductively 
from simple ideas and truths which seem to be 
ready in the mind, as in the case of the science 
of geometry, it may be that we have gathered 
those simple ideas and truths from previous ob- 
servation or induction of an almost unconscious 
kind. This is a debated point upon which I 
will not here speak positively ; but if the truth 
be as stated. Induction will be the mode by 
which all the materials of knowledge are brought 
to the mind and analysed. Deduction will then 
be the almost equally important procees by 
which the knowledge thus acquired is utilised, 
and by which new Inductions of a more compli- 
cated character, as we shall see, are rendered 
possible. 

An Induction, that is an act of Inductive 
reasoning, is called Perfect when all the possible 
cases or instances to which the conclusion can 
refer, have been examined and enumerated in the 
premises. If, as usually happens, it is impossi- 
ble to examine all cases, since they may occur at 
future times or in distant parts of the earth or 
other regions of the universe, the Induction is 
called Imperfect. The assertion that all the 
months of the year are of less length than thirty- 



310 QUOTATION'S Oi^ INDUCTION. 

two days is derived from Perfect Induction, and 
is a certain conclusion because the calendar is a 
human institution, so that we know beyond 
doubt how many months there are, and can 
readily ascertain that each of them is less than 
thirty-two days in length. But the assertion 
that all the planets move in one direction round 
the sun, from West to East, is derived from Im- 
perfect Induction ; for it is possible that there 
exist planets more distant than the most distant- 
known planet Neptune, and to such a planet of 
course the assertion would apply. 

Hence it is obvious that there is a great 
difference between Perfect and Imperfect Induc- 
tion. The latter includes some process by 
which we are enabled to make assertions concern- 
ing thino-s that we have never seen or examined 
or even known to exist. But it must be care- 
fully remembered also that no Imperfect Induc- 
tion can give a certain conclusion. It may be 
highly probable or nearly certain that the cases 
unexamined will resemble those which have been 
examined, but it can never be certain. It is 
quite possible, for instance, that a new planet 
might go round the sun in an opposite direction 
to the other planets. In the case of the satel- 
lites belonging to the planets more than one ex- 
ception of this kind has been discovered, and 
mistakes have constantly occurred in science 
from expecting that all new cases would exactly 
resemble old ones. Imperfect Induction thus 
gives only a certain degree of probability or like- 
lihood that all instances will ao:ree with those 



QUOTATIOi^S 01^ in'ductio:n'. 311 

examined. Perfect Induction, on tlie other hand, 
gives a necessary and certain conclusion, but it 
asserts nothing beyond what was asserted in the 
premises. 

Mr. Mill, indeed, differs from almost all other 
loo'icians in hoi dins: that Perfect Induction is 
improperly called Induction, because it does not 
lead to any new knowledge. He defines In- 
duction as inference from the known to the un- 
known, and considers the unexamined cases which 
are apparently brought into our knowledge as the 
only gain from the process of reasoning. Hence 
Perfect Induction seems to him to be of no scien- 
tific value whatever, because the conclusion is a 
mere reassertion in a briefer form, a mere sum- 
ming up of the premises. I may point out, how- 
ever, that if Perfect Induction were no more 
than a process of abbreviation it is yet of great 
importance, and requires to be continually used 
m science and common life. Without it we 
could never make a comprehensive statement, 
but should be obliged to enumerate every partic- 
ular. After examining the books in a library 
and finding them to be all English books we 
should be unable to sum up our results in the 
one proposition, " all the books in this library 
are English books ;" but should be required to go 
over the list of books every time we desired to 
make any one acquainted with the contents of 
the library. The fact is, that the power of ex- 
pressing a great number of particular facts in a 
very brief space is essential to the progress of 
science. Just as the whole science of arithmetic 



312 QUOTATIOITS Oiq" Il^TDUCTIOi^. 

consists in nothino; but a series of processes for 
abbreviating addition and subtraction, and enab- 
ling us to deal with a great number of units in a 
very short time, so Perfect Induction is abso- 
lutely necessary to enable us to deal with a great 
number of particular facts in a very brief space. 

It is usual to represent Perfect Induction in 
the form of an Inductive Syllogism, as in the 
following instance : — 
Mercury, Venus, the Earth, &c., all move round 

the sun from West to East. 
Mercury, Venus, the Earth, <fec., are all the 

known Planets. 
Therefore all the known planets move round the 

sun from West to East. 

This argument is a true Perfect Induction 
because the conclusion only makes an assertion 
of all knoiv7i planets, which excludes all refer- 
ence to possible future discoveries ; and we may 
suppose that all the known planets have been 
enumerated in the premises. . . . 

As another example of a Perfect Induction 
we may take — 

January, February, December, each con- 
tain less than 32 days. 
January December are all the months of 

the year. 
Therefore all the months of the year contain less 

than 32 days. 

Although Sir W. Hamilton has entirely 
rejected the notion, it seems worthy of inquiry 
whether the Inductive Syllogism be not really of 
the Disjunctive form of Syllogism. Thus I 



QUOTATIONS OK I1?"DUCTI0N". 313 

should be inclined to represent tlie last example 
in the form : 

A month of the year is either January, or 

February, or March or December ; but 

January has less than 32 days ; and February has 
less than 32 days ; and so on until we come to 
December, which has less than 32 days. 

It follows clearly that a month must in any 
case have less than 32 days ; for there are only 
12 possible cases, and in each case this is affirm- 
ed. The fact is that the major premise of the 
syllogism on the last page is a compound sen- 
tence with twelve subjects, and is therefore equi- 
valent to twelve distinct logical propositions. 
The minor premise is either a disjunctive propo- 
sition, as I have represented it, or something 
quite di'fierent from anything we have elsewhere 
had. 

From Perfect Induction we shall have to 
pass to Imperfect Induction ; but the opinions 
of Logicians are not in agreement as to the 
grounds upon which we are warranted in taking 
a part of the instances only, and concluding that 
what is true of those is true of all. Thus if we 
adopt the example fonnd in many books and 
say— 

This, that, and the other magnet attract iron ; 
This, that, and the other magnet are all magnets ; 
Therefore all magnets attract iron, 
we evidently employ a false minor premise, be- 
cause this, that, and the other magnet which we 
have examined, cannot possibly be all existing 
magnets. In whatever form we put it there 



314 QUOTATIOi^S Oiq- liTDUCTIOiq-. 

must be an assumption that tlie magnets "vvhicli 
we have examined are a fair specimen of all 
magnets, so that what we find in some we may 
expect in all. Archbishop Whately con- 
siders that this assumption should be expressed 
in one of the premises, and he represents Induc- 
tion as a Syllogism as follows : — 
That which belongs to this, that, and the other 

magnet, belongs to all ; 
Attracting iron belongs to this, that, and the 

other ; 
Therefore it belongs to all. 

But though this is doubtless a correct expression 
of the assumption made in an Imperfect Induc- 
tion, it does not in the least explain the grounds 
on which we are allowed to make the assump- 
tion, and under what circumstances such an as- 
sumption would be likely to prove true. Some 
writers have asserted that there is a Principle 
called the Uniformity of Nature, which enables 
us to affirm that what has often been found to 
be true of anything will continue to be found 
true of the same sort of thing. It must be ob- 
served, however, that if there be such a princi2^1e 
it is liable to exceptions ; for many facts which 
have held* true up to a certain point have after^ 
wards been found not to be always true. Thus 
there was a wide and unbroken induction tend- 
ing to show that all the Satellites in the plane- 
tary system went in one uniform direction round 
their planets. Nevertheless the Satellites of 
Uranus when discovered were found to move in 
a retrograde direction, or in an opposite direction 



qijotatio:n's oh iitductioit. 315 

to all Satellites previously known, and the same 
peculiarity attaches to the Satellite of Neptune 
more lately discovered. 

We may defer to the next lesson the ques- 
tion of the varying degree of certainty which be- 
longs to induction in the several branches of 
knowledge. 

The adv^anced student may consult the fol- 
lowing with advantage : — Mansel's Aldrich, Ap- 
pendix, Notes G- and H. Hamilton's Lectures 
on Logic, Lecture xvii., and Appendix vii., On 
Induction and Example, Vol. ii., p. 358. J. S. 
Mill's System of Logic, Book iii. Chap. 2, Of 
Inductions iiyiproperUj so-called, 

GEOMETKICAL AKD MATHEMATICAL IXDUC- 
TlOiq-, AJ^ALOGY AKD EXAMPLE. 

^ It is ^ now indispensable that we should con- 
sider with great care upon what grounds Imper- 
fect Induction is founded. No difficulty is en- 
countered in Perfect Induction because all possi- 
ble cases which can come under the general con- 
clusion are enumerated in the premises, so that 
in fact there is no information in tlie conclusion 
which was not given in the premises. In this 
respect the Inductive Syllogism perfectly agrees 
with the general principles of deductive reason- 
ing, which require that the information contain- 
ed in the conclusion should be shown onlv from 
the data, and that we should merely unfold, or 
transform into an explicit statement what is con- 
tained in the premises implicitly. 
In Imperfect Induction the process seems to 



ol6 quotatio:n-s oiq- ii^duction-. 

be of a wholly different cliaracter, since the in- 
stances concerning which we acquire knowledge 
may be infinitely more numerous than those from 
which we acquire the knowledge. Let ns con- 
sider in the tirst place the process of Geometrical 
Heasoning which has a close resemblance to in- 
ductive reasoning. When in the fifth proposi- 
tion of the first book of Euclid we prove that 
the angles at the base of an isosceles triangle are 
equal to each other, it is done by taking one par- 
ticular triangle as an example. A figure is given 
which the reader is requested to regard as having 
two equal sides, and it is conclusively proved 
that if the sides be really equal then the angles 
opposite to those sides must be equal also. But 
Euclid says nothing about other isosceles trian- 
gles ; he treats one single triangle as a sufiicient 
specimen of all isosceles triangles, and we are 
asked to believe that wliat is true of that is true 
of any other, whether its sides be so small as to 
be only visible in a microscope, or so large as to 
reach to the furthest fixed star. There may evi- 
dently be an infinite number of isosceles trian- 
gles as regards the length of the equal sides, and 
each of these may be infinitely varied by increas- 
ing or diminishing the contained angle, so that 
the number of possible isosceles triangles is infi- 
nitely infinite ; and yet we are asked to believe 
of this incomprehensible number of objects what 
we have proved only of one single specimen. 
This might seem to be the most extremely Im- 
perfect Induction possible, and yet every one al- 
lows that it gives us really certain knowledge. 



QUOTATIOJS-S 0>q- i:N-DUCTIOi^-. 317 

We do know with as mnch certainty as knowl- 
edge can possess, that if lines be conceived as 
drawn from the earth to two stars equally dis- 
tant, they will make equal angles with the line 
joining those stars ; and yet we can never have 
tried the experiment. 

The generality of this geometrical reasoning 
evidently depends upon the certainty with which 
we know that all isosceles triangles exactly resem- 
ble each other. The proposition proved does 
not in fact apply to a triangle unless it agrees 
with our specimen in all the qualities essentfal to 
the proof. The absolute length of any of the 
sides or the absolute magnitude of the angle con- 
tained between any of them were not points 
upon which the proof depended— they were 
purely accidental circumstances; hence we are 
at perfect liberty to apply to all new cases of an 
isosceles triangle what we learn of one case. 
Upon a similar ground rests all the vast body of 
certain knowledge contained in the mathematical 
sciences — not only all the geometrical truths, but 
all general algebraical truth. It was shown, for 
instance, in p. 58, that if a and b be two quan- 
tities, and we multiply together their sum and 
difference, we get the difference of the squares 
of a and b. However often we try this it will 
be found true ; thus if «r=10 and 6 = 7, the prod- 
uct of the sum and difference is I7x3=i51 • 
the squares of the quantities are 10x10 or 100 
and 7 X 7 or 49, the difference of which is also 
51. But however often we tried the rule no 
certainty would be added to it ; because when 



318 QUOTATIOKS 02^ INDUCTION. 

proved algebraically tliere was no condition 
whicli restricted the result to any particular num- 
bers, and a and h might consequently be any 
numbers whatever. This generality of algebraical 
reasoning by which a property is proved of infi- 
nite varieties of numbers at once, is one of the 
chief advantages of algebra over arithmetic. 
There is also in algebra a process called Mathe- 
matical Induction or Demonstrative Induction, 
which shows the powers of reasoning in a very 
conspicuous way. A good example is found in 
the following problem : — If we take the first Uvo 
consecutive odd numbers, 1 and 3, and add them 
together the sum is 4, or exactly hvice tivo ; if we 
take three such numbers l-|-3-|-5, the sum is 9 
or exactly three times three ; if we take four, 
namely l-f-S-j-S+V the sum is 16, or exactly 
four times four ; or generally, if we take any 
given number of the series, l-|-3-|-5-|-7-|-... 
the sum is equal to the number of the terms mul- 
tiplied by itself. Anyone who knows a very 
little algebra can prove that this remarkable law 
is universally true, as follows — Let n be the 
number of terms, and assume for a moment that 
this law is true up to n terms, thus — 

l4-3 + 5-|-'7+ -j-(2 n—\) = n\ 

Now add 2« + 1 to each side of the equation. 
It follows that — 

1 + 34-5 + 7+ +(2w-l) + (271 + 1) 

= ?i' + 2n + 1. 

But the last quantity n" -{-2n-{-l is just 



QUOTATIONS Oi^ IKDUCTIOK. 319 

equal to (7i-\-iy ; so that if the law is true for n 
terms it is true also for n-{-l terms. We are 
enabled to argue from each single case of the 
law to the next case ; but we have already shown 
that it is true of the first few cases, therefore it 
must be true of all. By no conceivable labor 
could a person ascertain by trial what is the sum 
of the first billion odd numbers, and yet symbol- 
ically or by general reasoning Ave know with cer- 
tainty that they would amount to a bilhon bil- 
lion, and neither more nor less even by a unit. 
This process of Mathematical Induction is not 
exactly the same as Geometrical Induction, be- 
cause each case depends upon the last, but the 
proof rests upon an equally narrow basis of ex- 
perience, and creates knowledge of equal cer- 
tainty and generality. 

Such mathematical truths depend upon ob- 
servation of a few cases, but they acquire cer- 
tainty from the perception we have of the exact 
similarity of one case to another, so that we un- 
doubtingly believe what is true of one case to be 
true of another. It is very instructive to con- 
trast with these cases certain other ones where 
there is a like ground of observation, but not 
the same tie of similarity. It was at one time 
believed that if any integral number were multi- 
pled by itself, added to itself and then added 
to 41, the result would be a prime number, that 
is a number which could not be divided by any 
other integral number except unity ; in symbols, 

cc^ -{- aj + 41 = prime number. 



320 quotatio:n's oiq" ikductioi?". 

This was believed solely on tlie ground of 
trial and experience, and it certainly holds for a 
great many values of x. Thus when x is suc- 
cessively made equal to the numbers in the first 
line below, the expression x^-\-x-\-4:l gives the 
values in the second line, and they are all prime 
numbers : 

012 3 456789 10 
41 43 47 63 61 71 83 97 113 131 151 

No reason however could be given why it 
should always be true, and accordingly it was 
found that the rule does not always hold true, 
but fails when a;=40. Then we have 40x40 
-j-40-|-41 = 1681, but this is clearly equal to 
41 X 40-J-41 or 41X41, and is not a prime num- 
ber. 

In that branch of mathematics which treats 
of the peculiar properties and kinds of numbers, 
other propositions depending solely upon obser- 
vation have been asserted to be always true. 

z 

Thus Fermat believed that 2^-1-1 always repre- 
sents a prime number, but could not give any 
reason for the assertion. It holds true in fact 
until the product reaches the large number 
4294967297, which was found to be divisible by 
641, so that the generality of the statement was 
disproved. 

We find then that in some cases a single in- 
stance proves a general and certain rule, while 
in others a very great number of instances are 
insufficient to give any certainty at all ; all de- 



QUOTATIONS OK IKDUCTIOiq-. 321 

pends upon tlie perception we have of similarity 
or identity between one case and another. We 
can perceive no similarity between all prime 
numbers which assures us that because one is 
represented by a certain formula, also another 
is ; but we do find such similarity between the 
sums of odd numbers, or between isosceles tri- 
angles. 

Exactly similar considerations apply to induc- 
tions in physical science. When a chemist an- 
alyses a few grains of water and finds that they 
contain exactly 8 parts of oxygen and 1 of hy- 
drogen for 9 parts of water, he feels warranted in 
asserting that the same is true of all pure water 
whatever be its origin, and whatever be the part 
of the world from which it comes. But if he 
analyse a piece of granite, or a sample of sea- 
water from one part of the world, he does not 
feel any confidence that it will resemble exactly 
a piece of granite, or a sample of sea-water from 
another part of the earth ; hence he does not 
venture to assert of all granite or sea- water, what 
he finds true of a single sample. Extended ex- 
perience shows that granite is very variable in 
composition, but that sea-water is rendered 
pretty uniform by constant mixture of currents. 
Nothing but experience in these cases could in- 
form us how far we may assert safely of one 
sample what we have ascertained of another. 
But we have reason to believe that chemical 
compounds are naturally fixed and invariable in 
composition, according to Dalton's laws of com- 
bining proportions. No a priori reasoning from 



322 QUOTATIONS OK INDUCTION?*. 

tlie principles of thouglit could have told us tLis, 
and we only learn it by extended experiment. 
But having once shown it to be true with certain 
substances we do not need to repeat the trial 
with all other substances, because we have every 
reason to believe that it is a natural law in which 
all chemical substances resemble each other. It 
is only necessary then for a single accurate anal- 
ysis of a given fixed compound to be made in 
order to inform us of the composition of all 
other portions of the same substance. 

It must be carefully observed however that 
all inductions in physical science are only- 
probable, or that if certain, it is only hypotheti- 
cal certainty they possess. Can I be absolutely 
certain that all water contains one part of hydro- 
gen in nine ? I am certain only on "Iwo condi- 
tions : — 

1. That this was certainly the composition of 
the sample tried. 

2. That any other substance I call water ex- 
actly resembles that sample. 

But even if the first condition be undoubtedly 
true, I cannot be certain of the second. For how 
do I know what is water except by the fact of 
its being a transparent liquid, freezing into a 
solid and evaporating into steam, possessing a 
liigh specific heat, and a number of other dis- 
tinct properties ? But can I be absolutely cer- 
tain that every liquid possessing all these proper- 
ties is water ? Practically I can be certain, but 
theoretically I cannot. 



QUOTATION'S OX INDUCTION". 323 

7. From Mill's Sijstem of Logic ^ pp. 125, 126 : 
210-228, 8vo edition. 

Reasoning, in the extended sense in which I 
use the. term, and in which it is synonymous 
with Inference, is popularly said to be of two 
kinds : reasoning from particulars to generals, 
and reasoning from generals to particulars ; 
the former being called Induction, the latter 
Ratiocination or Syllogism. It Avill presently 
be shown that there is a third species of rea- 
soning, which falls under neither of these de- 
scriptions, and which, nevertheless, is not only 
valid, but is the foundation of both the 
others. ... Of Induction, therefore, we 
shall say no more at present, than that it at least 
is, without doubt, a process of real inference. 
The conclusion in an induction embraces more 
than is contained in the premises. The principle 
or law collected from particular instances, the 
general proposition in which we embody the re- 
sult of our experience, covers a much larger ex- 
tent of ground than the individual experiments 
which form its basis. A principle ascertained by 
experience, is more than a mere summing up of 
what has been specifically observed in the indi- 
vidual cases which have been examined ; it is a 
generalization grounded on those cases, and ex- 
pressive of our belief, that what we there found 
true is true in an indefinite number of cases 
which we have not examined, and are never 
likely to examine. The nature and grounds of 
this inference, and the conditions necessary to 
make it legitimate, will be the subject of discus- 



324 quotatio:n"S ok ikductiok. 

sion in the Third Book : but that such inference 
really takes place is not susceptible of question. 
In every induction we proceed from truths ^Yhich 
Ave knew, to truths which we did not know ; 
from facts certified by observation, to facts 
which we have not observed, and even to facts 
not capable of being now observed ; future 
facts, for example ; but which we do not hesi- 
tate to believe on the sole evidence of the induc- 
tion itself. Induction, then, is a real process of 
Reasoning or Inference. 

OF INDUCTIONS IMPROPERLY SO CALLED. 

§ 1. Induction, then, is that operation of the 
mind, b}^ which we infer that what we know to be 
true in a particular case or cases, will be true in all 
cases which resemble the former in certain assign- 
able respects. In other words, Induction is the 
process by Avhich Ave conclude that Avhat is true 
of certain individuals of a class is true of the 
Avhole class, or that Avhat is true at certain times 
Avill be true in similar circumstances at all times. 

This definition excludes from the meaning of 
the term Induction, various logical operations, to 
Avliich it is not unusual to apply that name. 

Induction, as above defined, is a process of 
inference ; it proceeds from the known to the 
unknoAvn ; and any operation involving no infer- 
ence, any process in Avhich Avhat seems the con- 
clusion is no Avider than the premises from Avhich 
it is draAvn, does not fall Avithin the meaning of 
the term. Yet in the common books of Logic 
Ave find this laid doAvn as the most perfect, in- 



QUOTATIONS Oi^ IKDUCTIOJT. 325 

deed tlie only quite perfect, form of induction. 
In those books, every process which sets out 
from a less general and terminates in a more 
general expression — which admits of being stated 
in the form, " This and that A are B, therefore 
every A is B " — is called an induction, whether 
any thing be really concluded or not : and the 
induction is asserted not to be perfect, unless 
every single individual of the class A is included 
in the antecedent, or premise : that is, unless 
Avhat we affirm of the class has already been as- 
certained to be true of every individual in it, so 
that the nominal conclusion is not really a con- 
clusion, but a mere re-assertion of the premises. 
If we were to say. All the planets shine by the 
sun's light, from observation of each separate 
planet, or All the Apostles were Jews, because 
this is true of Peter, Paul, John, and every other 
apostle — these, and such as these, would, in the 
phraseology in question, be called perfect, and 
the only perfect. Inductions. This, however, is 
a totally different kind of induction from ours ; 
it is not an inference from facts known to facts 
unknown, but a mere short-hand registration of 
facts known. The two simulated arguments 
which we have quoted, are not generalizations ; 
the propositions purporting to be conclusions 
from them, are not really general propositions. 
A general proposition is one in which the predi- 
cate is affirmed or denied of an unlimited num- 
ber of individuals ; namely, all, whether few or 
many, existing or capable of existing, which pos- 
sess the properties connoted by the subject of 



326 QUOTATIONS Oi^ IKDUCTIOK. 

the proposition. " All men are mortal " does 
not mean all now living, but all men past, pres- 
ent, and to come. When the signification of 
the term is limited so as to render it a name not 
for any and every individual failing nnder a cer- 
tain general description, but only for each of a 
number of individuals, designated as such, and 
as it were, counted off individually, the proposi- 
tion, though it may be general in its language, 
is no general proposition, but merely that num- 
ber of singular propositions, written in an abridg- 
ed character. The operation may be very use- 
ful, as most forms of abridged notation are ; 
but it is no part of the investigation of truth, 
though often bearing an important part in the 
preparation of the materials for that investiga- 
tion. 

As we may sum up a definite number of singular 
propositions in one proposition, which will be 
apparently, but not really, general, so we may 
sum up a definite number of general proposi- 
tions in one proposition, which will be apparent- 
ly, but not really, more general. If by a sepa- 
rate induction applied to every distinct species of 
animals, it has been established that each pos- 
sesses a nervous system, and we afiirm thereupon 
that all animals have a nervous system ; this looks 
like a generalization, though as the conclusion 
merely affirms of all what has already been af- 
firmed of each, it seems to tell us nothing but what 
we knew before. A distinction, however, must 
be made. If in concluding that all animals have 
a nervous system, we mean the same thing and 



QUOTATIONS OK IKDUCTION". 327 

no more as if we had said " all known animals," 
the proposition is not general, and the process 
by which it is arrived at is not induction. But 
if our meaning is that the observations made of 
the various species of animals have discovered to 
us a law of animal nature, and that we are in a 
condition to say that a nervous system will be 
found even in animals yet undiscovered, this in- 
deed is an induction ; but in this case the general 
proposition contains more than the sum of the 
special propositions from which it is inferred. 
The distinction is still more forcibly brought out 
when we consider, that if this real generalization 
be legitimate at all, its legitimacy probably does 
not require that we should have examined with- 
out exception every known species. It is the 
number and nature of the instances, and not their 
being the whole of those which happen to be 
known, that makes them sufficient evidence to 
prove a general law : while the more limited as- 
sertion, which stops at all known animals, cannot 
be made unless we have rigorously verified it in 
every species. In like manner (to return to a 
former example) we might have inferred, not that 
all the planets, but that all planets, shine by re- 
flected light : the former is no induction ; the 
latter is an induction, and a bad one, being dis- 
proved by the case of double stars — self-lum- 
inous bodies which are properly planets, since 
they revolve round a centre. 

§ 2. There are several processes used in math- 
ematics which require to be distinguished from 
Induction, being not unfrequently cahed by that 



328 QUOTATIONS 01^ IN"DUCTIOiT. 

name, and being so far similar to Induction 
properly so called, that the propositions they 
lead to are really general propositions. For ex- 
ample, when we have proved with respect to 
the circle, that a straight line can not meet it in 
more than two points, and when the same thing 
has been successively proved of the ellipse, the 
parabola, and the hyperbola, it may be laid 
down as a universal property of the sections of 
the cone. The distinction drawn in the two 
previous examples can have no place here, there 
being no difference between all known sections 
of the cone and all sections, since a cone demon- 
strably can not be intersected by a plane except 
in one of these four lines. It would be diffi- 
cult, therefore, to refuse to the proposition ar- 
rived at, the name of a generalization, since 
there is no room for any generalization beyond 
it. But there is no induction, because there is 
no inference : the conclusion is a mere summing 
up of what was asserted in the various proposi- 
tions from which it is drawn. A case some- 
wdiat, though not altogether, similar, is the proof 
of a geometrical theorem by means of a diagram. 
Whether the diagram be on paper or only in the 
imagination, the demonstration (as formerly ob- 
served) does not prove directly the general theo- 
rem ; it proves only that the conclusion, which 
the theorem asserts generally, is true of the par- 
ticular triangle or circle exhibited in the diagram ; 
but since we perceive that in the same way in 
which we have proved it of that circle, it might 
also be proved of any other circle, we gather up 



QUOTATIO]S"S ON" INDUCTION. 329 

into one general expression all the singular prop- 
ositions susceptible of being thus proved, and 
embody them in a universal proposition. Hav- 
ing shown that the three angles of the triangle 
ABC are together equal to two right angles, we 
conclude that this is true of every other triangle, 
not because it is true of ABC, but for the same 
reason which proved it to be true of ABC. If 
this were to be called Induction, an appropriate 
name for it w^ould be, induction by parity of rea- 
soning. But the term can not properly belong 
t© it ; the characteristic quality of Induction is 
wanting, since the truth obtained, though really 
general, is not believed on the evidence of par- 
ticular instances. We do not conclude that all 
triangles have the property because some trian- 
gles have, but from the ulterior demonstrative 
evidence which was the ground of our conviction 
in the particular instances. 

There are nevertheless, in mathematics, some 
examples of so-called Induction, in which the 
conclusion does bear the appearance of a gener- 
alization grounded on some of the particular 
cases included in it. A mathematician, when he 
has calculated a sufficient number of the terms of 
an algebraical or arithmetical series to have ascer- 
tained w^hat is called the law of the series, does 
not hesitate to fill up any number of the suc- 
ceeding terms without repeating the calculations. 
But I apprehend he only does so when it is appa- 
rent from a priori considerations (which might 
be exhibited in the form of demonstration) that 
the mode of formation of the subsequent terms, 



330 QUOTATIOl^S OK IISTDUCTIOK. 

each from that which preceded it, must be simi- 
lar to the formation of the terms which have 
been already calculated. And when the attempt 
has been hazarded Avithout the sanction of such 
general considerations, there are instances on rec- 
ord in which it has led to false results. 

It is said that Newton discovered the binomial 
theorem by induction ; by raising a binomial 
successively to a certain number of powers, and 
comparing those powers with one another until 
he detected the relation in which the algebraic 
formula of each power stands to the exponent of 
that power, and to the two terms of the bino- 
mial. The fact is not improbable : but a math- 
ematician like Newton, who seemed to arrive i^^r 
saltum at principles and conclusions that ordinary 
mathematicians only reached by a succession of 
steps, certainly could not have performed the 
comparison in question without being led by it 
to the a i^riori ground of the law ; since any one 
who understands sufficiently the nature of multi- 
plication to venture upon multiplying several 
lines of symbols at one operation, can not but 
perceive that in raising a binomial to a power, 
the co-efficients must depend on the laws of per- 
mutation and combination : and as soon as this 
is recognized, the theorem is demonstrated. 
Indeed, when once it was seen that the law pre- 
vailed in a few of the lower poAvers, its identity 
with the law of permutation would at once sug- 
gest the considerations which prove it to obtain 
universally. Even, therefore, such cases as 
these, are but examples of what I have called In- 



QUOTATIONS OK IKDUCTIOK. 331 

duction by parity of reasoning, that is, not really 
Induction, because not involving inference of a 
general proposition from particular instances. 

§ 3. There remains a third improper use of 
the term Induction, which it is of real impor- 
tance to clear up, because the theory of Induction 
has been, in no ordinary degree, confused by it, 
and because the confusion is exemplified in the 
most recent and elaborate treatise on the induc- 
tive philosophy which exists in our language. 
The error in question is that of confounding a 
mere description, by general terms, of a set of 
observed phenomena, with an induction from 
them. 

Suppose that a phenomenon consists of parts, 
and that these parts are only capable of being 
observed separately, and as it were piecemeal. 
When the observations have been made, there is 
a convenience (amounting for many purposes to 
a necessity) in obtaining a representation of the 
phenomenon as « whole, by combining, or as we 
may say, piecing these detached fragments to- 
gether. A navigator sailing in the midst of the 
ocean discovers land : he can not at first, or by any 
one observation, determine whether it is a conti- 
nent or an island ; but he coasts along it, and 
after a few days finds himself to have sailed com- 
pletely round it : he then pronounces it an island. 
Now there was no particular time or place of ob- 
servation at which he could perceive that this 
land was entirely surrounded by water : he as- 
certained the fact by a succession of partial ob- 
servations, and then selected a general expression 



332 QUOTATIONS OIT IKDUCTIOK. 

"vvliicli summed up in two or three words the 
whole of what he so observed. But is there any 
thing of the nature of an induction in this pro- 
cess ? Did he infer any thing that had not been 
observed, from something else which had ? Cer- 
tainly not. He had observed the whole of what 
the proposition asserts. That the land in ques- 
tion is an island, is not an inference from the 
partial facts which the navigator saw in the 
course of his circumnavigation ; it is the facts 
themselves ; it is a summary of those facts ; the 
description of a complex fact, to which those 
simpler ones are as the parts of a whole. 

Now there is, I conceive, no difference in kind 
between this simple operation, and that by which 
Kepler ascertained the nature of the planetary 
orbits : and Kepler's operation, all at least that 
was characteristic in it, was not more an induc- 
tive act than that of our supposed navij^ator. 

The object of Kepler was to determine the 
real path described by each of the planets, or let 
us say by the planet Mars (since it was of that 
body that he first established the two of his three 
laws which did not require a comparison of plan- 
ets). To do this there was no other mode than 
that of direct observation : and all which obser- 
vation could do was to ascertain a great number 
of the successive places of the planet ; or rather, 
of its apparent places. That the planet occupied 
successively all these positions, or at all events, 
positions which produced the same impressions 
on the eye, and that it passed from oae of these 
to another insensibly, and without any apparent 



QUOTATIOiq"S OK INDUCTlOi^-. 333 

breach of continuity ; thus much the senses, 
with the aid of the proper instruments, could 
ascertain. Wliat Kepler did more than this, 
was to find what sort of a curve these different 
points would make, supposing them to be all 
joined together. He expressed the whole series 
of the observed places of Mars by what Dr. Whe- 
well calls the general conception of an ellipse. 
This operation was far from being as easy as 
that of the navigator who expressed the series of 
his observations on successive points of the 
coast by the general conception of an island. 
But it is the very same sort of operation ; and if 
the one is not an induction but a description, 
this must also be true of the other. 

The only real induction concerned in the case, 
consisted in inferring that because the observed 
places of Mars were correctly represented by 
points in an imaginary ellipse, therefore Mars 
would continue to revolve in that same ellipse ; 
and in concluding (before the gap had been 
filled up by further observations) that the posi- 
tions of the planet during the time which inter- 
vened between two observations, must have coin- 
cided with the intermediate points of the curve. 
For these were facts which had not been directly 
observed. They were inferences from the obser- 
vations ; facts inferred, as distinguished from 
facts seen. But these inferences were so far from 
being a part of Kepler's philosophical operation, 
that they had been drawn long before he was 
born. Astronomers had long known that the 
planets periodically returned to the same places. 



334 QUOTATIONS Q-^ IKDUCTIOK. 

Wlien this had been ascertained, there was no 
induction left for Kepler to make, nor did he 
make any further induction. He merely applied 
his new conception to the facts inferred, as he 
did to the facts observed. Knowing already that 
the planets continued to move in the same paths ; 
when he found that an ellipse correctly repre- 
sented the past path, he knew that it would rep- 
resent the future path. In finding a compen- 
dious expression for the one set of facts, he 
found one for the other : but he found the ex- 
pression only, not the inference ; nor did he 
(which is the true test of a general truth) add 
any thing to the power of prediction already 
possessed. 

§ 4. The descriptive operation which enables 
a number of details to be summed up in a single 
proposition, Dr. Whewell, by an aptly chosen 
expression, has termed the Colligation of Facts. 
In most of his observations concerning that men- 
tal process I fully agree, and would gladly trans- 
fer all that portion of his book into my own 
pages. I only think him mistaken in setting up 
this kind of operation, which according to the 
old and received meaning of the term, is not in- 
duction at all, as the type of induction generally; 
and laying down, throughout his work, as prin- 
ciples of induction, the principles of mere colli- 
gation. 

Dr. AVhewell maintains that the general prop- 
osition which binds together the particular 
facts, and makes them, as it were, one fact, is 
not the mere sum of those facts, but something 



QUOTATIONS 02?[ INDUCTIOIj^. 335 

more, since there is introduced a conception of 
tlie mind, which did not exist in the facts them- 
selves. " The particular facts, " says he,* " are 
not merely brought together, but there is a new ele- 
ment added to the combination by the very act of 
thought by which they are combined. 
When the Greeks, after long observing the mo- 
tions of the planets, saw that these motions' 
might be rightly considered as produced by the 
motion of one wheel revolving in the inside of an- 
other wheel, these wheels were creations of their 
minds, added to the facts which they perceived 
by sense. And even if the wheels were no 
longer supposed to be material, but were reduced 
to mere geometrical spheres or circles, they were 
not the less products of the mind alone — some- 
thing additional to the facts observed. The 
same is the case in all other discoveries. The 
facts are known, but they are insulated and un- 
connected, till the discoverer supplies from his 
own store a principle of connection. The pearls 
are there, but they will not hang together till 
some one provides the string." 

Let me first remark that Dr. Whewell, in this 
passage, blends together, indiscriminately, ex- 
amples of both the processes which I am endeav- 
oring to distinguish from one another. When 
the Greeks abandoned the supposition that the 
planetary motions were produced by the revo- 
lution of material wheels, and fell back upon the 
idea of "mere geometrical spheres or circles," 

* Novum Organum Renovatum, pp. 72, 73. 



336 QUOTATIOITS OK IKDUCTIOIT. 

there was more in tliis change of opinion than 
the mere substitution of an ideal curve for a 
physical one. There was the abandonment of a 
theory, and the replacement of it by a mere de- 
scription. No one would think of calling the 
doctrine of material wheels a mere description. 
That doctrine was an attempt to point out the 
force by which the planets were acted upon, and 
compelled to move in their orbits. But when, 
by a great step in philosophy, the materiality of 
the wheels was discarded, and the geometrical 
forms alone retained, the attempt to account for 
the motions was given up, and what was left of 
the theory was a mere description of the orbits. 
The assertion that the planets were carried round 
by wheels revolving in the inside of other 
wheels, gave place to the proposition, that they 
moved in the same lines which would be traced 
by bodies so carried : which was a mere mode 
of representing the sum of the observed facts ; 
as Kepler's was another and a better mode of 
representing the same observations. 

It is true that for these simply descriptive op- 
erations, as well as for the erroneous inductive 
one, a conception of the mind was required. 
The conception of an ellipse must have presented 
itself to Kepler's mind, before he could identify 
the planetary orbits with it. According to Dr. 
"Whewell, the conception was something added 
to the facts. He expresses himself as if Kepler 
had put something into the facts by his mode 
of conceiving them. But Kepler did no such 
thing. The ellipse was in the facts before Kep- 



QUOTATIONS OK INDUCTION". 337 

ler recognized it ; just as the island was an island 
before it had been sailed round. Kepler did 
not 2^ut what he had conceived into the facts, but 
saw it in them. A conception implies, and cor- 
responds to, something conceived : and though 
the conception itself is not in the facts, but in 
our mind, yet if it is to convey any knowledge 
relating to them, it must be a conception of 
something which really is in the facts, some pro- 
perty which they actually possess, and which 
they would manifest to our senses, if our senses 
were able to take cognizance of it. If, for in- 
stance, the planet left behind it in space a visible 
track, and if the observer were in a fixed posi- 
tion at such a distance from the plane of the 
orbit as would enable him to see the whole of it 
at once, he would see it to be an eUipse ; and if 
gifted with appropriate instruments and powers 
of locomotion, he could prove it to be such by 
measuring its different dimensions. Nay, fur- 
ther : if the track were visible, and he were so 
placed that he could see all parts of it in succes- 
sion, but not all of them at once, he might be 
able, by piecing together his successive observa- 
tions, to discover both that it was an ellipse and 
that the planet moved in it. The case would 
then exactly resemble that of the navigator who 
discovers the land to be an island by sailing 
round it. If the path was visible, no one I 
think would dispute that to identify it with an 
ellipse is to describe it : and I can not see why 
any difference should be made by its not being 



338 QUOTATIONS OK IKDUCTIOIf, 

directly an object of sense, when every point in it 
is as exactly ascertained as if it were so. 

Subject to the indispensable condition which 
has just been stated, I do not conceive that the 
part which conceptions have in the operation of 
studying; facts, has ever been overlooked or un- 
dervalued. No one ever disputed that in order 
to reason about any thing we must have a concep- 
tion of it ; or that when we include a multitude 
of things under a general expression, there is im- 
plied in the expression a conception of something 
common to those things. But it by no means 
follows that the conception is necessarily pre-ex- 
istent, or constructed by the mind out of its own 
materials. If the facts are rightly classed under 
the conception, it is because there is in the facts 
themselves something of which the conception is 
itself a copy ; and which if we can not directly 
perceive, it is because of the limited power of 
our organs, and not because the thing itself is not 
there. The conception itself is often obtained 
by abstraction from the very facts which, in Dr. 
"Whewell's language, it is afterward called in to 
connect. This he himself admits, when he ob- 
serves (which he does on several occasions), how 
great a service would be rendered to the science 
of physiology by the philosopher ' ' who should 
establish a precise, tenable, and consistent con- 
ception of life." * Such a conception can only 
be abstracted from the phenomena of life itself ; 
from the very facts which it is put in requisition 

* Novum Organum Benovatum, p. 32. 



QUOTATIONS OlS" INDUCTION. 339 

to connect. In other cases, no doubt, instead of 
collecting tlie conception from the very phenom- 
ena which we are attempting to colligate, we se- 
lect it from among those which have been pre- 
viously collected by abstraction from other facts. 
In the instance of Kepler's laws,, the latter was 
the case. The facts being out of the reach of 
being observed, in any such manner as would have 
enabled the senses to identify directly the path of 
the planet, the conception requisite for framing 
a general description of that path could not be 
collected by abstraction from the observations 
themselves ; the mind had to supply hypotheti- 
cally, from among the conceptions it had ob- 
tained from other portions of its experience, 
some one which would correctly represent the 
series of the observed facts. It had to frame a 
supposition respecting the general course of the 
phenomenon, and ask itself, If this be the general 
description, what will the details be ? and then 
compare these with the details actually observed. 
If they agreed, the hypothesis would serve for a 
description of the phenomenon : if not, it was 
necessarily abandoned, and another tried. It is 
such a case as this which gives rise to the doc- 
trine that the mind, in framing the descriptions, 
adds something of its own which it does not find 
in the facts. 

Yet it is a fact surely, that the planet does 
describe an ellipse ; and a fact which we could 
see, if we had adequate visual organs and a suit- 
able position. Not having these advantages, but 
possessing the conception of an ellipse, or (to ex- 



340 QUOTATIONS OlSr II^DUCTIOK. 

press tlie meaning in less technical language) 
knowing what an ellipse was, Kepler tried 
whether the observed places of the planet were 
consistent with such a path. He found they 
were so ; and he, consequently, asserted as a 
fact that the planet moved in an ellipse. But 
this fact, which Kepler did not add to, but found 
in, the motions of the planet, namely, that it 
occupied in succession the various points in the 
circumference of a given ellipse, was the very 
fact, the separate parts of which had been sepa- 
rately observed ; it was the sum of the different 
observations. 

Having stated tliis fundamental difference be- 
tween mv opinion and that of Dr. Whewell, I 
must add, that his account of the manner in 
which a conception is selected, suitable to ex- 
press the facts, appears to me perfectly just. 
The experience of all thinkers will, I believe, 
testify that the process is tentative ; that it con- 
sists of a succession of guesses ; many being re- 
jected, until one at last occurs fit to be chosen. 
We know from Kepler himself that before hitting 
upon the " conception" of an ellipse, he tried 
nineteen other imaginary paths, which, finding 
them inconsistent with the observations, he was 
obliged to reject. But, as Dr. AVhewell truly 
says, the successful hypothesis, though a guess, 
ought generally to be called, not a lucky, but a 
skillful guess. The guesses which serve to give 
mental unity and wholeness to a chaos of 
scattered particulars, are accidents which rarely 
occur to any minds but those abounding in 



QUOTATIONS OIT IKDUCTIOI^". 341 

knowledge and disciplined in intellectual combi- 
nations. 

How far this tentative metliod, so indispens- 
able as a means to the colligation of facts for 
purposes of description, admits of application to 
Induction itself, and what functions belong to it 
in that department, will be considered in the 
chapter of the present Book which relates to 
Hypotheses. On the present occasion we have 
chiefly to distinguish this process of Colligation 
from Induction properly so called ; and that the 
distinction may be made clearer, it is well to ad- 
vert to a curious and interesting remark, which 
is as strikingly true of the former operation, as 
it appears to me unequivocally false of the latter. 

In different stages of the progress of knowledge, 
philosophers have employed, for the colligation 
of the same order of facts, different conceptions. 
The early rude observations of the heavenly 
bodies, in which minute precision was neither 
attained nor sought, presented nothing inconsist- 
ent with the representation of the path of a 
planet as an exact circle, having the earth for its 
centre. As observations increased in accuracy, 
facts were disclosed which were not reconcilable 
with this simple supposition : for the colligation 
of those additional facts, the supposition was 
varied ; and varied again and again as facts be- 
came more numerous and precise. The earth 
was removed from the centre to some other 
point within the circle ; the planet was supposed 
to revolve in a smaller circle called an epicycle, 
round an imaginary point which revolved in a 



342 QUOTATIOiq-S OK IKDUCTIOK. 

circle round the earth : in proportion as observa- 
tion elicited fresh facts contradictory to these 
representations, other epicycles and other eccen- 
trics were added, producing additional complica- 
tion ; until at last Kepler swept all these circles 
away, and substituted the conception of an exact 
ellipse. Even this is found not to represent with 
complete correctness the accurate observations of 
the present day, which disclose many slight de- 
viations from an orbit exactly elliptical. Now 
Dr. Whewell has remarked that these successive 
general expressions, though apparently so con- 
flicting, were all correct : they all answered the 
purpose of colligation ; they all enabled the 
mind to represent to itself with facility, and by 
a simultaneous glance, the whole body of facts 
at the time ascertained : each in its turn served 
as a correct description of the phenomena, so far 
as the senses luid up to that time taken cogni- 
zance of them. If a necessity afterward arose 
for discarding one of these general descriptions 
of the planet's orbit, and framing a different 
imaginary line, by which to express the series of 
observed positions, it was because a number of 
new facts had now been added, which it was 
necessary to combine with the old facts into one 
general description. But this did not affect the 
correctness of the former expression, considered 
as a general statement of the only facts which it 
was intended to represent. And so true is this, 
that, as is well remarked by M. Comte, these 
ancient generalizations, even the rudest and most 
imperfect of them, that of uniform movement in 



QUOTATIONS OK IKDUCTIOK. 343 

a circle, are so far from being entirely false, 
that they are even now habitually employed by 
astronomers when only a rough approximation 
to correctness is required. " L'astronomie mod- 
erne, en detruisant sans retour les hypotheses 
primitives, envisagees comme lois reelles du 
monde, a soigneusement maintenu leur valeur 
positive et permanente, la propriete de repre- 
senter commodement les phenomenes quand il 
s'agit d'une premiere ebauche. Nos ressources a 
cet egard sont meme bien plus etendues, precise- 
ment a cause que nous ne nous faisons aucune 
illusion sur la realite des hypotheses ; ce qui 
nous permet d' employer sans scrupule, en chaque 
cas, celle que nous jugeons la plus avantageuse.'"'^ 

Dr. Whe well's remark, therefore, is philo- 
sophically correct. Successive expressions for 
the colligation of observed facts, or, in other 
words, successive descriptions of a phenomenon 
as a whole, which has been observed only in 
parts, may, though conflicting, be all correct as 
far as they go. But it would surely be absurd 
to assert this of conflicting inductions. 

The scientific study of facts may be under- 
taken for three different purposes : the simple 
description of the facts ; their explanation ; or 
their prediction : meaning by prediction, the de- 
termination of the conditions under which sim- 
ilar facts may be expected again to occur. To 
the first of these three operations the name of 
Induction does not properly belong : to the 

* Cours ^6 Philosophie Positive, vol. ii., p. 203. 



344 QUOTATIONS OK Il^DUCTIOl!^. 

other two it does. Now, Dr. Wliewell's obser- 
vation is true of tlie first alone. Considered as 
a mere description, the circular theory of the 
heavenly motions represents perfectly well their 
general features : and by adding epicycles with- 
out limit, those motions, even as now known to 
us, might be expressed with any degree of accu- 
racy that might be required. The elliptical 
theory, as a mere description, would have a great 
advantage in point of simplicity, and in the con- 
sequent facility of conceiving it and reasoning 
about it ; but it would not really be more true 
than the other. Different descriptions, there- 
fore, may be all true : but not, surely, different 
explanations. The doctrine that the heavenly 
bodies moved by a virtue inherent in their celes- 
tial nature ; the doctrine that they were moved 
by impact (which led to the hypothesis of vor- 
tices as the only impelling force capable of 
whirling bodies in circles), and the Newtonian 
doctrine, that they are moved by the composi- 
tion of a centripetal with an original projectile 
force ; all these are explanations, collected by 
real induction from supposed parallel cases ; and 
they were all successively received by philoso- 
phers, as scientific truths on the subject of the 
heavenly bodies. Can it be said of these, as 
was said of the different descriptions, that they 
are all true as far as they go ? Is it not clear 
that only one can be true in any degree, and 
the other two must be altogether false ? So 
much for explanations : let us now compare 
different predictions : the first, that eclipses will 



QUOTATIONS OK Il^DUCTIOK. 345 

occur when one planet or satellite is so situated 
as to cast its shadow upon another ; the second, 
that they will occur when some great calamity is 
impending over mankind. Do these two doc- 
trines only differ in the degree of their truth, as 
expressing real facts with unequal degrees of ac- 
curacy ? Assuredly the one is true, and the 
other absolutely false.* 

* Dr. Wliewell, in his reply, contests the distinction 
here drawn, and maintains, that not only different 
descriptions, but different explanations of a phenom- 
enon, may all be true. Of the three theories respect- 
ing the motions of the heavenly bodies, he says {Phi- 
losox)hy of Discovery, p. 281) : " Undoubtedly, all these 
explanations may be true and consistent with each 
other, and would be so if each had been followed out 
so as to show in what manner it could be made con- 
sistent with the facts. And this was, in reality, in a 
great measure done. The doctrine that the heavenly 
bodies were moved by vortices was successfully mod- 
ified, so that it came to coincide in its results with 
the doctrine of an inverse-quadratic centripetal force. 
. . . When this point was reached, the vortex was 
merely a machinery, well or ill devised, for produc- 
ing such a centripetal force, and therefore did not con- 
tradict tlie doctrine of a centripetal force. Newton 
himself does not appear to have been averse to ex- 
plaining gravity by impulse. So little is it true that 
if one theory be true the other must be false. The 
attempt to explain gravity by the impulse of streams 
of particles flowing through the universe in all direc- 
tions, which I have mentioned in the Philosophy, is so 
far from being consistent with the Newtonian theory, 
that it is founded entirely upon it. And even with 
regard to the doctrine, that the heavenly bodies move 
by an inherent virtue ; if this doctrine had been main- 
tained in any such way that it was brought to agree 



346 QUOTATIONS OK IKDUCTIOIT. 

In every way, tlierefoi'e, it is evident that to 
explain induction as the colligation of facts by 

with the facts, the inherent virtue must have had its 
laws determined ; and then it w^ould have been found 
that the virtue had a reference to the central body ; 
and so, the ' inherent virtue ' must have coincided in 
Its effect with the Newtonian force ; and then, the two 
explanations would agree, except so far as the word 
' inherent ' was concerned. And if such a part of an 
earlier theory as this word inherent indicates, is found 
to be untenable, it is of course rejected in the transi- 
tion to later and more exact theories, in Inductions 
of this kind, as well as in what Mr. Mill calls De- 
scriptions. There is, therefore, still no validity dis- 
coverable in the distinction which Mr. Mill attempts to 
draw between descriptions like Kepler's law of ellip- 
tical orbits, and other examples of induction." 

If the doctrine of vortices had meant, not that vor- 
tices, existed but only that the planets moved in the 
same manner as if they had been wiiirled by vortices ; 
if the hypothesis had been merely a mode of repre- 
senting the facts, not an attenij^t to account for them ; 
if, in fe'liort, it had been only a Desciiption ; it would, 
no doubt, have been reconcilable with the Newtonian 
theory. The vortices, however, were not a mere aid 
to conceiving the motions of the planets, but a sup- 
posed physical agent, actively impelling them ; a 
material fact, which might be true or not true, Ijut 
could not be both true and not true. According to 
Descartes's theory it was true, according to Newton's 
it was not true. Dr. Whewell probably means that 
since the phrases, centripetal and projectile force, do 
not declare the nature but only the direction of tlie 
forces, the Newtonian theory does not absolutely 
contradict any hypothesis which may be framed re- 
specting the mode of their production. The New- 
tonian theory, regarded as a mere descri'ption of the 
planetary motions, does not ; but the Newtonian 
theory as an explanation of them does. For in what 



QUOTATIONS ON INDUCTION. 347 

means of appropriate conceptions, that is, con- 
ceptions which will really express them, is to 

does the explanation consist ? In ascribing those 
motions to a general law which obtains between all 
particles of matter, and in identifying this with the 
law by which bodies fall to the ground. If the 
planets are kept in their orbits by a force which 
draws the particles composing them toward every 
other particle of matter in the solar system, they are 
not kept in those orbits by the impulsive force of 
certain streams of matter which whirl them round. 
The one explanation absolutely excludes the other. 
Either the planets are not moved by vortices, or they 
do not move by a law common to all matter. It is 
impossible that both opinions can be true. As well 
might it be said that there is no contradiction be- 
tween the assertions, that a man died because some- 
body killed him, and that he died a natural death. 

So, again, the theory that the planets move by a 
virtue inherent in their celestial nature, is incom- 
. patible with either of the two others : eitlier that of 
their being moved by vortices, or that which regards 
them as moving by a property which they have in 
common with the earth and all terrestrial bodies. 
Dr. Whewell says that the theory of an inherent 
virtue agrees with Newton's when the word inherent 
is left out, which of course it would be (he says) if 
"found to be untenable." But leave that out, and 
where is the theory? The word inherent is the 
theory. When that is omitted, there remains nothing 
except that the heavenly bodies move " by a virtue,'' 
i.e., by a power of some sort ; or by virtue of their 
celestial nature, which directly contradicts the doc- 
trine that terrestrial bodies fall by the same law. 

If Dr. Whewell is not yet satisfied, any other sub- 
ject will serve equally well to test his doctrine. He 
will hardly say that there is no contradiction between 
the emission theory and the undulatory theory of 
light : or that there can be both one and two electric- 



348 QUOTATIONS OH IKDUCTIOK. 

confound mere description of the observed facts 
with inference from those facts, and ascribe to 

ities ; or that the hypothesis of the production of the 
higher organic forrns by development from the lower, 
and the supposition of separate and successive acts of 
creation, are quite reconcilable ; or that the theory 
that volcanoes are fed from a central fire, and the 
doctrines which ascribe them to chemical action at a 
comparatively small depth below the earth's surface, 
are consistent with one another, and all true as far as 
they go. 

If different explanations of the same fact can not 
both be true, still less, surely, can different predic- 
tions. Dr. Whewell quarrels (on what ground it is 
not necessary here to consider) with the example I 
had chosen on this point, and thinks an objection to 
an illustration a sufiicient answer to a theory. Ex- 
amples not liable to his objection are easily found, 
if tlie proposition that conflicting predictions can not 
both be true, can be made clearer by any examples. 
Suppose the phenomenon to be a new^ly-discovered 
comet, and that one astronomer predicts its return 
once in every 300 years — another once in every 400 : 
can they botli be right ? When Columbus predicted 
that by sailing constantly westward he should in 
time return to the point from which he set out, while 
others asserted that he could never do so except by 
turning back, were both he and his opponents true 
prophets ? Were the predictions which foretold the 
wonders of railwaj^s and steamships, and those which 
averred that the Athnntic could never be crossed by 
stpnm navigation, nor a railway train propelled ten 
miles an hour, both (in Dr. Whewell's words) " true, 
and consistent with one another?" 

Dr. Whewell sees no distinction between holding 
contradictory opinions on a question of fact, and 
merely employing different analogies to facilitate the 
conception of the same fact. The case of different 
Inductions belongs to the former class, that of differ- 
ent Descriptions to the latter. 



QUOTATIONS OK INDUCTION". 349 

the latter what is a characteristic property of the 
former. 

There is, however, between Colligation and 
Induction, a real correlation, Avhich it is impor- 
tant to conceive correctly. Colligation is not 
always induction ; but induction is always colli- 
gation. The assertion that the planets move in 
ellipses, was but a mode of representing observed 
facts ; it was but a colligation ; while the asser- 
tion that they are drawn, or tend, toward the 
sun, was the statement of a new fact, inferred 
by induction. But the induction, once made, 
accomplishes the purposes of colligation likewise. 
It brings the same facts, which Kepler had con- 
nected by his conception of an ellipse, under the 
additional conception of bodies acted upon by a 
central force, and serves, therefore, as a new 
bond of connection for those facts ; a new prin- 
ciple for their classification. 

Further, the descriptions which are improp- 
erly confounded with induction, are nevertheless 
a necessary preparation for induction ; no less 
necessary than correct observation of the facts 
themselves. Without the previous colligation of 
detached observations by means of one general 
conception, we could never have obtained any 
basis for an induction, except in the case of 
phenomena of very limited compass. We should 
not be able to affirm any predicates at all, of a 
subject incapable of being observed otherwise 
than piecemeal : much less could we extend those 
predicates by induction to other similar subjects. 
Induction, therefore, always presupposes, not 



350 QUOTATIOI^S ON INDUCTIOI^". 

only tliat the necessary observations are made 
with tlie necessary accuracy, but also that the 
results of these observations are, so far as prac- 
ticable, connected together by general descrip- 
tions, enabling the mind to represent to itself 
as wholes whatever phenomena are capable of 
being so represented. 

§ 5. Dr. Whewell has replied at some length 
to the preceding observations, restating his opin- 
ions, but without (as far as I can perceive) add- 
ing any thing material to his former arguments. 
Since, however, mine have not had the good for- 
tune to make any impression upon him, I will 
subjoin a few remarks, tending to show more 
clearly in what our difference of opinion consists, 
as well as, in some measure, to account for it. 

Nearly all the definitions of induction, by 
writers of authority, make it consist in drawing 
inferences from known cases to unknown ; 
affirming of a class, a predicate which has been 
found true of some cases belonging to the class ; 
concluding because some things have a certain 
property, that other things which resemble them 
have the same property — or because a thing has 
manifested a property at a certain time, that it 
has and will have that property at other times. 

It will scarcely be contended that Kepler's 
operation was an Induction in this sense of the 
term. The statement, that Mars moves in an 
elliptical orbit, was no generalization from indi- 
vidual cases to a class of cases. Neither was it 
an extension to all time, of what had been found 
true at some particular time. The whole amount 



QUOTATIOK^S ON INDUCTIONS". 351 

of generalization which the case admitted of, 
was already completed, or might have been so. 
Long before the elliptic theory was thought of, 
it had been ascertained that the planets returned 
periodically to the same apparent places ; the 
series of these places was, or might have been, 
completely determined, and the apparent course 
of each planet marked out on the celestial globe 
in an uninterrupted line. Kepler did not extend 
an observed truth to other cases than those in 
which it had been observed : he did not widen 
the subject of the proposition which expressed 
the observed facts. The alteration he made was 
in the predicate. Instead of saying, the suc- 
cessive places of Mars are so and so, he summed 
them up in the statement, that the successive 
places of Mars are pomts in an ellipse. It is 
true, this statement, as Dr. Whewell says, was 
not the sum of the observations merely ; it -was 
the sum of the observations seen uncle?' a new point 
of view. ^ But it was not the sum of more than 
the observations, as a real induction is. It took 
in no cases but those Avhich had been actually ob- 
served, or which could have been inferred from 
the observations before the new point of view 
presented itself. There was not that transition 
from known cases to unknown, which constitutes 
Induction in the original and acknowledged 
meaning of the term. 

Old definitions, it is true, can not prevail 
against new knowledge : and if the Keplerian 

* FMl ofBiscov., p. 256. 



352 QUOTATIONS OK II^DUCTIOK. 

operation, as a logical process, be really identical 
with what takes place in acknowledged induc- 
tion, the definition of induction ought to be so 
widened as to take it in ; since scientific language 
ought to adapt itself to the true relations which 
subsist between the things it is employed to des- 
ignate. Here then it is that I am at issue with 
Dr. Whewell. He does think the operations 
identical. He allows of no logical process in 
any case of induction, other than what there was 
in Kepler's case, namely, guessing until a guess 
is found which tallies with the facts ; and ac- 
cordingly, as we shall see hereafter, he rejects all 
canons of induction, because it is not by means 
of them that we guess. Dr. Whewell's theory 
of the logic of science would be very perfect if 
it did not pass over altogether the question of 
Proof. But in my apprehension there is such a 
thing as proof, and inductions difPer altogether 
from descriptions in their relation to that ele- 
ment. Induction is proof ; it is inferring some- 
thing unobserved from something observed : it 
requires, therefore, an appropriate test of proof ; 
and to provide that test, is the special purpose 
of inductive logic. When, on the contrary, we 
merely collate known observations, and, in Dr. 
Whewell's phraseology, connect them by means 
of a new conception ; if the conception does 
serve to connect the observations, we have all 
we want. As the proposition in which it is em- 
bodied pretends to no other truth than what it 
may share with many other modes of represent- 
ing the same facts, to he consistent with the facts 



QUOTATIONS ON" IKDUCTION. 353 

is all it requires : it neither needs nor admits 
of proof ; though it may serve to prove other 
things, inasmuch as, by placing the facts in 
mental connection with other facts, not previ- 
ously seen to resemble them, it assimilates the 
case to another class of phenomena, concerning 
which real Inductions have already been made. 
Thus Kepler's so-called law brought the orbit of 
Mars into the class ellipse, and by doing so, 
proved all the properties of an ellipse to be true 
of the orbit : but in this proof Kepler's law sup- 
plied the minor premise, and not (as is the case 
with real Inductions) the major. 

Dr. Whewell calls nothing Induction where 
there is not a new mental conception introduced, 
and every thing induction where there is. But 
this is to confound two very different things, In- 
vention and Proof. The introduction of a new 
conception belongs to Invention : and invention 
may be required in any operation, but is the es- 
sence of none. A new conception may be intro- 
duced for descriptive purposes, and so it may for 
inductive purposes. But it is so far from con- 
stituting induction, that induction does not nec- 
essarily stand in need of it. Most inductions 
require no conception but what was present in 
every one of the particular instances on which 
the induction is grounded. That all men are 
mortal is surely an inductive conclusion ; yet no 
new conception is introduced by it. AVhoever 
knows that any man has died, has all the concep- 
tions involved in the inductive generalization. But 
Dr. Whewell considers the process of invention 



354 QUOTATIONS OK IKDUCTIOK. 

wiiicli consists in framing a new conception con- 
sistent witli the facts, to be not merely a neces- 
sary part of all induction, but the whole of it. 

The mental operation which extracts from a 
number of detached observations certain general 
characters in which the observed phenomena re- 
semble one another, or resemble other known 
facts, is what Bacon, Locke, and most subse- 
quent metaphysicians, have understood by the 
word x\bstraction. A general expression ob- 
tained by abstraction, connecting known facts 
by means of common characters, but without 
concluding from them to unknown, may, I 
think, with strict logical correctness, be termed 
a Description ; nor do I know in what other way 
things can ever be described. My position, how- 
ever, does not depend on the employment of that 
particular word ; I am quite content to use Dr. 
Whewell's term Colligation, or the more gen- 
eral phrases, ' mode of representing, or of ex- 
pressing, phenomena : ' provided it be clearly 
seen that the process is not Induction, but 
something radically different. 

What more may usefully be said on the subject 
of Colligation, or of the correlative expression 
invented by Dr. Whewell, the Explication of 
Conceptions, and generally on the subject of 
ideas and mental representations as connected 
with the study of facts, will find a more appro- 
priate place in the Fourth Book, on the Opera- 
tions Subsidiary to Induction : to which I must 
refer the reader for the removal of any difficulty 
which the present discussion may have left. 



QUOTATIONS ON IKDUCTION. 355 



OF THE GROUND OF INDUCTION. 

§ 1. Induction properly so called, as dis- 
tmgiiislied from those mental operations, some- 
times, though improperly, designated by the 
name, which I have attempted in the preceding 
chapter to characterize, may, then, be summarily 
defined as Generalization from Experience. ^ It 
consists in inferring from some individual in- 
stances in which a phenomenon is observed to 
occur, that it occurs in all instances of a certain 
class ; namely, in all Avhich reseinhle the former, 
in what are regarded as the material circum- 
stances. 

In what way the material circumstances are 
to be distinguished from those which are imma- 
terial, or why some of the circumstances are ma- 
terial and others not so, we are not yet ready to 
point out. We must first observe, that there is 
a principle implied in the very statement of what 
Induction is ; an assumption with regard to the 
course of nature and the order of the universe ; 
namely, that there are such things in nature as 
parallel cases ; that what happens once, will, 
under a suflicient degree of similarity of circum- 
stances, happen again, and not only again, but 
as often as the same circumstances recur. This, 
I say, is an assumption, involved in every case 
of induction. And, if we consult the actual 
course of nature, avc find that the assumption is 
warranted. The universe, so far as known to 
us, is so constituted, that whatever is true in 
any one case, is true in all cases of a certain de- 



356 QUOTATIONS ON INDUCTION. 

scription ; tlie only difficulty is, to find what de- 
scription. 

This universal fact, which is our warrant for 
all inferences from experience, has heen de- 
scribed by different philosophers in different 
forms of language : that the course of nature is 
uniform ; that the universe is governed by gen- 
eral laws ; and the like. One of the most usual 
of these modes of expression, but also one of 
the most inadequate, is that which has been 
brought into familiar use by the metaphysicians 
of the school of Reid and Stewart. The dispo- 
sition of the human mind to generalize from ex- 
perience — a propensity considered by these phi- 
losophers as an instinct of our nature — they usu- 
ally describe under some such name as ' ' our in- 
tuitive conviction that the future will resemble 
the past." Now it has been well pointed out by 
Mr. Bailey,* that (whether the tendency be or 
not an original and ultimate element of our na- 
ture), Time, in its modifications of past, present, 
and future, has no concern either with the belief 
itself, or with the grounds of it. We believe 
that fire will burn to-morrow, because it burned 
to-day and yesterday ; but we believe, on pre- 
cisely the same grounds, that it burned before we 
were born, and that it burns this very day in 
Cochin-China. It is not from the past to the 
future, as past and future, that we infer, but from 
the known to the unknown ; from facts observed 
to facts unobserved ; from what we have per- 

* Essays on tJie Pursuit of Truth. 



QUOTATIONS ON INDUCTION. 357 

ceived, or been directly conscious of, to what has 
not come within our experience. In this last 
predicament is the whole region of the future ; 
but also the vastly greater portion of the present 
and of the past. 

Whatever be the most proper mode of express- 
ing it, the proposition that the course of nature 
is uniform, is the fundamental principle, or gen- 
eral axiom, of Induction. It would yet be a 
great error to offer this large generalization as 
any explanation of the inductive process. On the 
contrary, I hold it to be itself an instance of in- 
duction, and induction by no means of the most 
obvious kind. Far from being the first induction 
we make, it is one of the last, or at all events one 
of those which are latest in attaining strict phil- 
osophical accuracy. As a general maxim, indeed, 
it has scarcely entered into the minds of any but 
philosophers; nor even by them, as we shall have 
many opportunities of remarking, have its extent 
and limits been always very justly conceived. 
The truth is, that this great g:eneralization is itself 
founded on prior generalizations. The obscurer 
laws of nature were discovered by means of it, 
but the more obvious ones must have been under- 
stood and assented to as general truths before it 
w^as ever heard of. We should never have thought 
of affirming that all phenomena take place ac- 
cording to general laws, if we had not first arrived, 
in the case of a gcreat multitude of phenomena, 
at some knowledge of the laws themselves ; which 
could be done no otherwise than by induction. 
In what sense, then, can a principle, which is so 



358 QUOTATIONS OK INDUCTION. 

far from being our earliest induction, be regarded 
as our warrant for all the others ? In the only- 
sense, in which (as we have already seen) the 
general propositions w^hich we place at the head 
of our reasonings when we throw them into syl- 
logisms, ever really contribute to their validity. 
As Archbishop Whately remarks, every induction 
is a syllogism with the major premise suppress- 
ed ; or (as I prefer expressing it) every induction 
may be thrown into the form of a syllogism, by 
supplying a major premise. If this be actually 
done, the principle which we are now considering, 
that of the uniformity of the course of nature, 
will appear as the ultimate major premise of all 
inductions, and will, therefore, stand to all in- 
ductions in the relation in which, as has been 
shown at so much length, the major proposition 
of a syllogism always stands to the conclusion ; 
not contributing at all to prove it, but being a 
necessary condition of its being proved ; since no 
conclusion is proved, for which there can not be 
found a true major premise.* 

* In the first edition a note was appended at (his 
place, containing some criticism on Archhisliop's 
Whately's mode of conceiving the relation between 
Syllogism and Induction. In a subsequent issue of 
his Logic, tlie Archbishop made a reply to the criti- 
cism, which induced me to cancel part of the note, 
incorporating the remainder in the text. In a still 
later edition^ the Archbishop observes in a tone of 
something like disapprobation, that the objections, 
" doubtle'ss from their being fully answered and 
found untenable, were silently suppressed," and that 
hence he might appear to some of his readers to be 



QUOTATIONS OiT I:N"DUCTI0]S'. 359 

The statement, that the uniformity of the course 
of nature is the ultimate major premise in all cases 



combating a shadow. On this latter point, the Arch- 
bishop need give himself no uneasiness. His readers, 
I make bold to say, will fully credit his mere affirm- 
ation that the objections have actually been made. 

But as he seems to think that what he terms the 
suppression of the objections ought not to have been 
made "silently," I now break that silence, and 
state exactly what it is that 1 suppressed, and why. 
I suppressed that alone which might be regarded as 
personal criticism on the Archbishop. I had imput- 
ed to him the having omitted to ask himself a partic- 
ular question. I found that he had asked himself the 
question, and could give it an answer consistent with 
his own theory. I had also, within the compass of a 
parenthesis, hazarded some remarks on certain general 
characteristics of Archbishop Whately as a philoso- 
pher. These remarks, though their tone, I hope, was 
neither disrespectful nor arrogant, I lelt, on recon- 
sideration, that I was hardly entitled to make ; least 
of all, when the instance which 1 had regarded as an 
illustration of them, failed, as I now saw, to bear 
them out. The real matter at the bottom of the 
whole dispute, the different view we take of the 
function of the major premise, remains exactly where 
it was ; and so far was I from thinking that my 
opinion had been fully " answered" and was "un- 
tenable," that in the same edition in which I can- 
celled the note, I not only enforced the opinion by 
faither arguments, but answered (though without 
naming him) those of the Archbishop. 

For not having made this statement before, I do 
not think it needful to apologize. It would be at- 
taching very great importance to one's smallest say- 
ings, to think a formal retractation requisite every 
time that one falls into an error. Nor is Archbishop 
Whately's well-earned fame of so tender a quality as 



360 QUOTATION'S OIT liTDUCTIOK. 

of induction, may be thouQ^ht to require some 
explanation. The immediate major premise in 
every inductive argument, it certainly is not. Of 
that, Archbishop Whately 's must be held to be the 
correct account. The induction, '' John, Peter, 
etc., are mortal, therefore all mankind are mor- 
tal," may, as he justly says, be thrown into a syl- 
logism by prefixing as a major premise (what is at 
any rate a necessary condition of the validity of 
the argument), namely, that what is true of John 
Peter, etc., is true of all mankind. But how 
came we by this major premise ? It is not self- 
evident ; nay, in all cases of unwarranted gene- 
ralization, it is not true. How, then, is it arrived 
at ? Necessarily either by induction or ratioci- 
nation ; and if by induction, the process, like all 
other inductive arguments, may be thrown into 
the form of' a syllogism. This previous syllogism 
it is, therefore, necessary to construct. There is, 
in the long run, only one possible construction. 
The real proof that what is true of John, Peter, 
etc., is true of all mankind, can only be, that a 
different supposition would be inconsistent with 
the uniformity which we know to exist in the 
course of nature. Whether there would be this 
inconsistency or not, may be a matter of long and 
delicate inquiry ; but unless there would, we have 
no sufficient ground for the major of the induct- 
ive syllogism. It hence appears, that if we throw 
the whole course of any inductive argument into 

to require that in withdrawing a slight criticism on 
him I should have been bound to offer a public 
amende for having made it. 



QUOTATIONS ON" INDUCTION. 361 

a series of syllogisms, we shall arrive by more or 
fewer steps at an ultimate syllogism, which will 
have for its major premise the principle, or axi- 
om, of the uniformity of the course of nature.* 
It was not to be expected that in the case of 
this axiom, any more than of other axioms, there 
should be unanimity among thinkers with respect 
to the grounds on which it is to be received as 
true. I have already stated that I regard it as 

* But though it is a condition of the validity of 
every induction that there be uniformity in the course 
of nature, it is not a necessary condition that the uni- 
formity should pervade all nature. It is enough that 
it pervades the particular class of phenomena to 
which the induction relates. An induction concern- 
ing the motions of the planets, or the properties of the 
magnet, would not be vitiated though we were to sup- 
pose that wind and weather are the sport of chance, 
provided it be assumed that astronomical and mag- 
netic phenomena are under the dominion of general 
laws. Otherwise the early experience of mankind 
would have rested on a very weak foundation ; for 
in the infancy of science it could not be known that 
all phenomena are regular in their course. 

Neither would it be correct to say that every induc- 
tion by which we infer any truth, implies the general 
fact of uniformity as foreknoicn, even in reference to 
the kind of phenomena concerned. It implies, either 
that this general fact is already known, or that we 
may now know it : as the conclusion, the Duke of 
"Wellington is mortal, drawn from the instances A, B, 
and C, implies either that we have already concluded 
all men to be mortal, or that we are now entitled to 
do so from the same evidence. A vast amount of 
confusion and paralogism respecting the grounds of 
Induction would be dispelled by keeping in view 
these simple considerations. 



362 QUOTATIONS OK lis^DUCTION. 

itself a generalization from experience. Others 
hold it to be a principle which, antecedently to 
any verification by exj^erience, we are compelled 
by the constitution of our thinking faculty to as- 
sume as true. Having so recently, and at so 
much length, combated a similar doctrine as ap- 
plied to the axioms of mathematics, by arguments 
which are in a great measure applicable to the 
present case, I shall defer the more particular 
discussion of this controverted point in regard to 
the fundamental axiom of induction, until a more 
advanced period of our inquiry. At present it 
is of more importance to understand thoroughly 
the import of the axiom itself. For the propo- 
sition, that the course of nature is uniform, pos- 
sesses rather the brevity suitable to popular, than 
the precision requisite in philosophical language : 
its terms require to be explained, and a stricter 
than their ordinary signification given to them, 
before the truth of the assertion can be admitted. 
§ 2. Every person's consciousness assures him 
that he does not always expect uniformity in the 
course of events ; he does not always beheve that 
the unknown wdll be similar to the known, that 
the future will resemble the past. Nobody be- 
lieves that the succession of rain and fine weather 
will be the same in every future year as in the 
present. Nobody expects to have the same 
dreams repeated every night. On the contrary, 
every body mentions it as something extraordi- 
nary, if the course of nature is constant, and re- 
sembles itself, in these particulars. To look for 
constancy where constancy is not to be expected, 



Q,UOTATIOl!^S Oiq- INDUCTIOiq-. 363 

as for instance that a day wliicli has once brought 
good fortune will always be a fortunate day, is 
justly accounted superstition. 

The course of nature, in truth, is not only uni- 
form, it is also infi?iitely various. Some phenom- 
ena are always seen to recur in the very same 
combinations in which we met with them at first; 
others seem altogether capricious ; while some, 
which we have been accustomed to regard as bound 
down exclusively to a particular set of combina- 
tions, we unexpectedly find detached from some 
of the elements with whicli we had hitherto found 
them conjoined, and united to others of quite a 
contrary description. To an inhabitant of Central 
Africa, fifty years ago, no fact probably appeared 
to rest on more uniform experience than this, 
that all human beings are black. To Europeans, 
not many years ago, the proposition. All swans 
are white, appeared an equally unequivocal in- 
stance of uniformity in the course of nature. 
Further experience has proved to both that they 
were mistaken ; but they had to wait fifty centu- 
ries for this experience. During that long time, 
mankind believed in a uniformity of the course 
of nature where no such uniformity really existed. 

According to the notion which the ancients en- 
tertained of induction, the foregoing were cases 
of as legitimate inference as any inductions what- 
ever. In these two instances, in which, the con- 
clusion being false, the ground of inference must 
have been insufficient, there was, nevertheless, as 
much ground for it as this conception of induction 
admitted of. The induction of the ancients has 



364 QUOTATIONS OK INDUCTION?'. 

been well described by Bacon, under the name 
of " Inductio per ennmerationem simplicem, ubi 
non reperitur instantia contradictoria. ' ' It con- 
sists in ascribing the character of general truths to 
all propositions which are true in every instance 
that we happen to know of. This is the kind of 
induction which is natural to the mind when un- 
accustomed to scientific methods. The tendency, 
which some call an instinct, and which others 
account for by association, to infer the future 
from the past, the known from the unknown, is 
simply a habit of expecting that what has been 
found true once or several times, and never yet 
found false, will be found true again. Whether 
the instances are few or many, conclusive or in- 
conclusive, does not much affect the matter : 
these are considerations which occur only on re- 
flection ; the unprompted tendency of the mind 
is to generalize its experience, provided this points 
all in one direction ; provided no other experience 
of a conflicting character comes unsought. The 
notion of seeking it, of experimenting for it, of 
mterrogating nature (to use Bacon's expression) 
is of much later growth. The observation of na- 
ture, by uncultivated intellects, is purely passive : 
they accept the facts which present themselves, 
without taking the trouble of searching for more : 
it is a superior mind only which asks itself what 
facts are needed to enable it to come to a safe 
conclusion, and then looks out for these. 

But though we have always a propensity to 
generalize from unvarying experience, we are not 
always warranted in doing so. Before we can b.e 



QUOTATIOKS OK IKDUCTIOiT. 365 

at liberty to conclude that sometliing is univers- 
ally true because we have never known an instance 
to the contrary, we must have reason to believe 
that if there were in nature any instances to the 
contrary, we should have known of them. This 
assurance, in the great majority of cases, we can 
not have, or can have only in a very moderate 
degree. The possibility of having it, is the 
foundation on which we shall see hereafter that 
induction by simple enumeration may in some 
remarkable cases amount practically to proof. 
No such assurance, however, can be had, on any 
of the ordinary subjects of scientific inquiry. 
Popular notions are usually founded on induction 
by simple enumeration ; in science it carries us 
but a little way. We are forced to be.2;in with 
it ; we must often rely on it provisionally, in the 
absence of means of more searching investigation. 
But, for the accurate study of nature, we require 
a surer and a more potent instrument. 

It was, above all, by pointing out the insuf- 
ficiency of this rude and loose conception of In- 
duction, that Bacon merited the title so generally 
awarded to him, of Founder of the Inductive 
Philosophy. The value of his own contributions 
to a more philosophical theory of the subject has 
certainly been exaggerated. Although (along with 
some fundamental errors) his writings contain, 
more or less fully developed, several of the most 
important principles of the Inductive Method, 
physical investigation has now far outgrown the 
Baconian conception of Induction. Moral and 
political inquiry, indeed, are as yet far behind 



3G6 QUOTATIONS OK IKDUCTIOH. 

that conception. The current and apj)roved 
modes of reasoning on these subjects are still of 
the same vicious description against which Bacon 
protested ; the method almost exclusively em- 
ployed by those professing to treat such matters 
inductively, is the very inductio per enumerationem 
simjjlicem which he condemns ; and the experi- 
ence which we hear so confidently appealed to by 
all sects, parties, and interests, is still, in his own 
emphatic words, 7nera palpatio. 

§ 3. In order to a better understanding of the 
problem which the logician must solve if he 
would establish a scientific theory of Induction, 
let us compare a few cases of incorrect inductions 
with others which are acknowledged to be legiti- 
mate. Some, we know, which were believed for 
centuries to be correct, were nevertheless incor- 
rect. That all swans are white, can not have 
been a good induction, since the conclusion has 
turned out erroneous. The experience, however, 
on which the conclusion rested, was genuine. 
From the earliest records, the testimony of the 
inhabitants of the known world was unanimous 
on the point. The uniform experience, therefore, 
of the inhabitants of the known world, agreeing 
in a common result, without one known instance 
of deviation from that result, is not always suffi- 
cient to establish a general conclusion. 

But let us now turn to an instance apparently 
not very dissimilar to this. Mankind were wTong, 
it seems, in concluding that all swans were white : 
are we also wrong, when we conclude that all 
men's heads grow above their shoulders, and 



QUOTATIOIs"S OH IN"DUCTIOK. 367 

never below, in spite of tlie conflicting testimony 
of the naturalist Pliny ? As there were black 
swans, though civihzed people had existed for 
three thousand years on the earth without meet- 
ing with them, may there not also be " men 
whose heads do grow beneath their shoulders, ' ' 
notwithstanding a rather less perfect unanimity 
of negative testimony from observers ? Most 
persons would answer No ; it was more credible 
that a bird should vary in its color, than that men 
should vary in the rehxtive position of their prin- 
cipal organs. And there is no doubt that in so 
saying they would be right : but to say why they 
are right, would be impossible, without entering 
more deeply than is usually done into the true 
theory of Induction. 

Again, there are cases in which we reckon with 
the most unfailing confidence upon uniformity, 
and other cases in which we do not count upon it 
at all. In some we feel complete assurance that 
the future will resemble the past, the unknown 
be precisely similar to the known. In others, 
however invariable may be the result obtained 
from the instances which have been observed, we 
draw from them no more than a very feeble pre- 
sumption that the like result will hold in all other 
cases. That a straight line is the shortest dis- 
tance between two points, we do not doubt to be 
true even in the reo-ion of the fixed stars. "^ When 



* In strictness, wherever the present constitution 
of space exists ; which we have ample reason to 
believe that it does in the reign of the fixed stars. 



368 QUOTATIONS OK Il^DUCTIOK. 

a chemist announces the existence and properties 
of a newly-discovered substance, if we conlide in 
his accuracy, we feel assured that the conchisions 
he has arrived at will hold universally, though the 
induction be founded but on a single instance. 
We do not withhold our assent, waiting for a 
repetition of the experiment ; or if we do, it is 
from a doubt whether the one experiment was 
properly made, not whether if properly made it 
would be conclusive. Here, then, is a general law 
of nature, inferred without hesitation from a 
single instance ; a universal proposition from a 
singular one. Now mark another case, and con- 
trast it with this. Not all the instances which 
have been observed since the beginning of the 
world, in support of the general proposition that 
all crows are black, would be deemed a sufficient 
presumption of the truth of the proposition, to 
outweigh the testimony of one unexceptionable 
witness who should affirm that in some region of 
the earth not fully explored, he had caught and 
examined a crow, and had found it to be gray. 

Why is a single instance, in some cases, suffi- 
cient for a complete induction, while in others, 
myriads of concurring instances, without a single 
exception known or presumed, go such a very little 
way toward establishing a universal proposition ? 
Whoever can answer this question knows more 
of the philosophy of logic than the wisest of the 
ancients, and has soked the problem of induction. 

(pp. 431-432). What renders arithmetic the 
type of a deductive science, is the fortunate ap- 
plicability to it of a law so comprehensive as 



QUOTATIOIiJ-S OK Il^DUCTIOiq-. 369 

*' The sums of equals are equals": or (to express 
the same principle in less familiar but more char- 
acteristic language), whatever is made up of 
parts, is made up of the parts of those parts. 
This truth, obvious to the senses in all cases which 
can be fairly referred to their decision, and so 
general as to be co- extensive with nature itself, 
being true of all sorts of phenomena (for all ad- 
mit of being numbered), must be considered an 
inductive truth, or law of nature, of the highest 
order. And every arithmetical operation is an 
application of this law, or of other laws capable 
of being deduced from it. This is our warrant 
fof all calculations. We believe that five and two 
are equal to seven, on the evidence of this in- 
ductive law, combined with the definitions of 
those numbers. We arrive at that conclusion (as 
all know who remember how they first learned it) 
by adding a single unit at a time : 5-|-l = 6, 
therefore 5-|-l-|-l = 6-|-l = 7 ; and again 2 = 1 
+1, therefore 5-f2=:5+l+l = 7. 



QUOTATIONS ON INTERPRETATION. 

APPENDIX J. 

234. 1. From Davies and Peck, Dictionary 
of Mathefiiatics. 

Interpretation. [L. interpretatio, explana- 
tion]. The process of explaining results arrived 
at by the application of mathematical rules. 
When, for example, an algebraic definition is 
laid down, there is frequently some restriction 
implied in making the definition, so that the re- 
sult to which it leads presents more cases than can 
be explained by it, or even than was contemplated 
by it. Thus the abbreviation of a a, a a a, into 
a^, a', and the rules which spring from it, lead 
to results of the form. 

a -% a^y a^% a ~ ^^, etc. 

These results, until interpreted, are without any 
intellio-ent algebraic meanina;. 

When such results arise, the province of inter- 
pretation begins ; their meaning and force are 
investigated and explained, and the definitions 
heretofore too narrow, are extended so as to cover 
these and other results. 

The rule to be adopted in interpreting new ex- 
pressions obtained by applying known processes, 
is to attribute to them such a meaninj^ as to make 



QUOTATIONS OliT IKTEKPRETATIOK. 371 

the whole of the process true by which they were 
obtained. For example : the formula 

a™ X «" = «"" "^ " 

is perfectly intelligible so long as m and n are 
whole numbers. Suppose it were required to in- 
terpret the symbol a", that is, to give to it such 
a meaning, that the above formula shall be true 
in that case. Making m = 0, the formula becomes 

a"" X «" = ^'^ + " = «" ; 

hence, a'' = 1. Again, suppose it were required 
to interpret the symbol a^. Make m = |- and 
n = "I, and the formula becomes 

a^ X «^^ = ci^' + ^- = a, 
hence, a^ = V«, for ^a x ^ct = «, by definition. 

Besides the application of the principles of in- 
terpretation to the explanation of new symbols, 
another very important application consists in 
making suppositions upon certain arbitrary quan- 
tities which enter formulas, and then comparing 
the results with known facts, thus deducing new 
truths. As an example of this method of inter- 
pretation let us take the equation of the ellipse 

a' f + K-x' = a' b\ 

and suppose cc > a, finding the value of y in 
terms of cc, we have 

y= ±~sla'-x\ 



372 QUOTATIOKS OK IKTERPEETATIOK. 

from "wliich we see that for all values of x greater 
than a, y is imaginary. Now an imaginary 
result indicates an impossibility in the assumption. 
Hence, we interpret the result as indicating that 
no point of the ellipse can lie at a greater distance 
from its conjugate axis than the extremity of the 
transverse axis. 

In integrating the differential of a transcen- 
dental function by an algebraic rule, a result oo is 
reached, which is manifestly absurd, since no 
function can be oo. We interpret this as indi- 
cating that the rale fails in the case considered. 

2. From Smith's Synonyms Discriminated. 

Expound (Lat. expono) denotes sustained ex- 
planation ; while a mere word or phrase may 
be explained, a whole work or parts of it may 
be expounded. Exposition is continuous crit- 
ical explanation. Interpret (Lat. interpres, 
an interpreter), beyond the mere sense of verbal 
translation from one language to another, conveys 
the idea of private or personal explanation of 
what is capable of more than one view. Hence 
interpretation is more arbitrary than exposition, 
and more theoretical than explanation. Expound 
relates only to words in series, interpretation is 
applicable also to anything of a symbolical char- 
acter, as to interpret a dream or a prophecy. It 
is also, in common with explain, an application 
to anything which may be viewed in different 
lights, as the actions of men. In this way, to 
explain conduct would rather be to account for 
it ; to interpret it would be to assign motives or 
significance to it. Explanation deals with facts, 
interpretation with causes also. 



QUOTATIONS ON DEDUCTION. 

APPENDIX K. 

235. 1. From Fleming's Vocabulary of Phi- 
losophy, Ed. 1858, pp. 126-7. 

Deduction (from deduce, to draw from, to 
cause to come out of,) is the mental operation 
which consists in drawing a particular truth from 
a general principle antecedently known. It is 
opposed to induction, which consists in rising 
from particular truths to the determination of 
a general principle. Let it be proposed to prove 
that Peter is mortal ; I know that Peter is a 
man, and this enables me to say that all men are 
mortal, from which affirmation I deduce that 
Peter is mortal. 

The syllogism is the form of deduction. Aris- 
totle (Prior. Analyt.,\\\). 1, cap. 1) has defined 
it to be " an enunciation in which certain asser- 
tions being made, by their being true, it follows 
necessarily, that another assertion different from 
the first is true also." 

Before we can deduce a particular truth, we 
must be in possession of the general truth. This 
may be acquired intuitively, as every change 
implies a cause ; or inductively, as the volume 
of gas is in the inverse ratio of the pressure. 

Deduction, when it uses the former kind of 



374 QUOTATIONS OK DEDUCTIOiT. 

truths, is demonstration or science. Truths 
drawn from the latter kind are contingent and 
relative, and admit of correction by increasing 
knowledge. The principle of deduction is, that 
things that agree with the same things agree with 
one another. The principle of induction is, that 
in the same circumstances, and in the same sub- 
stances, from the same causes the same efiects 
will follow. 

The mathematical and metaphysical sciences 
are founded on deduction, the physical sciences 
rest on induction. 

2. From Day's Elements of Logic, Ed. 1868, 
p. 105. 

A Deductive Syllogism is a Mediate Reasoning 
in which the movement of Thought is from a 
"Whole to a Part, mediated through a middle 
term, which is, respectively, a part of that wdiob 
and a whole of that part ; as, Man is m.ortal ; Caius 
is a man ; therefore, Caius is mortal. 

As the Deductive Syllogism is a Mediate 
Reasoning, its datum must consist of two Judg- 
ments, which, as given to Thought, are not of 
course at all validated by the Reasoning. 

They must be regarded consequently as only 
assumed for the Reasoning, or must rest on evi- 
dence foreign to it. But the movement of 
Thought in itself may be valid, although the given 
Judgments are false ; just as an arithmetical pro- 
cess may be correct, although applied to unreal 
objects. 

3. From Bowen's Logic, Ed. 1874, pp. 261, 
262. 



QUOTATIONS Oiq" DEDUCTION. 375 

Reasoning, liowever, proceeds not only in dif- 
ferent wholes, but in different aspects of the same 
whole. We may, it is evident, regard any whole, 
considered as the complement of its parts, in 
either of two ways ; for we may, on the one hand, 
look from the whole to the parts, and reason ac- 
cordingly downwards ; or, on the other hand, look 
from the parts to the whole they constitute, and 
reason accordingly upwards. The former of these 
reasonings is called Deductive, the latter Induc- 
tive. Deductive reasoning is founded on the 
maxim, ' What belongs to the containing whole 
belongs also to the contained parts ;' Induction, 
on the contrary maxim, ' What belongs to the 
constituent parts belongs also to the constituted 
whole.' Thus, in Deductive reasoning, the 
whole is stated first, and what is affirmed of it is 
affirmed of the parts it contains ; in other words, 
a general law is laid down, and predicated of the 
particular instances to which it applies. 

In Inductive reasoning, the parts are first stated, 
and what is predicated of them is also predicated 
of the whole they constitute ; in other words, the 
particular instances are first stated as facts, and 
then the law they constitute is evolved. 

4. From Hedge's Elements of Logick, Ed. 
1854, pp. 118, 119. 

Syllogism (=Deduction) and induction pro- 
ceed in opposite directions. Induction . . begins 
with individual objects, as they exist in nature, 
and ascends by successive steps to the most 
general truths. Syllogism (= Deduction) begins 
where inductions terminates. It commences with 



376 QUOTATIONS OK DEDUCTIOi^. 

some universal proposition, and follows back tlie 
footsteps of the former process, transferring at 
each stage the predicate of the more general to 
the less general rank of beings ; or, in other 
words, predicating the genus of the species, and 
the species of the individual. 

. . . Syllogism (= Deduction) is employed 
with advantage in communicating to others, in 
an exact and perspicuous manner, the general 
principles of science. It may also be used with 
success in exposing the weakness of arguments, 
stated in loose or figurative language. But it 
is of no service in helping us to the discovery 
of new truths. ' ' We must know a thing first, ' * 
Mr. Locke observes, " and then we can prove it 
sjllogistically. ' ' 



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Bible in the Public Schools (The). Argu- 
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Cyclopaedia of Education (The). Edited by 

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Deaf and Dumb. See Latham, Reet, Scott. 

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Dickens (Chas.) Schools and School-masters. 
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Home. 120. New York. i 50 

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DOUAI (A.) A Reform of the Common English 
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Dunn (H.) Principles of Teaching. I2«. Lon- 
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DUPANLOUP (Monseigneur). The Child. Trans- 
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son. 120. Boston. I 50 

DvviGHT (B. W.) Higher Christian Education. 
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Education in Ireland. Thirty-seventh Report 
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Education in Japan. A Series of Letters ad- 
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Educational Year Book. 1873. 120. New 

York. I 00 

Eggleston (G. C.) How to Educate Yourself. 
A complete Guide to Students, showing how to Study, 
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Ellis (W.) Education as a Means of Preventing 
Destitution. 8**. London. I 60 



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tilation. 4". New York. 6 oo 

Everett (Edward). Importance of Practical Ed- 
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Examiner (The), or Teacher's Aid. 12°. Cin- 
cinnati. 50 

FARRAR (F. W.) Essays on a Liberal Educa- 
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Fichte (J. G.) On the Nature of the Scholar and 
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New York. 15 

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80. London. I 75 

Five Hundred Mistakes of Daily Occurrence in 

Speaking, Pronouncing and Writing the English Lan- 
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Forrester (A.) The Teacher's Text-book. 8°. 

Halifax. 4 00 

Foster (J.) On the Evils of Popular Ignorance. 

12^ New York. i 25 

Four Years at Yale. By a Graduate of '69. 

12°. New Haven. 4 00 



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Frankland (Ed.) How to Teach Chemistry. 
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ROBISHER (J. E.) Selected Readings, Serious 
and Humorous, in Prose and Poetry, with an Appen- 
dix on Elocution, etc. 12^. Syracuse. 

Paper, 0.25; boards, 50 

Fry (Herbert). Our Schools and Colleges, giving 
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institutions. 12". London, 1867. 2 00 

Fuller (Thos.) The History of the University 
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FURNIVALL (Fr. J.) Education in Early England. 
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GARVEY (M. A.) A Manual of Human Culture. 
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to Observe and Think. 160. London. I 00 

Systems of Education. A History and 

Criticism. 12". London. I 40 

GiLMORE (J. H.) Outlines of the Art of Expres- 
sion. 12''. Boston. I 25 

Gow (A. M.) Good Morals and Gentle Manners 
for Schools and Families. 12". Cincinnati. I 25 

Grant (Horace). Exercises for the improvement 
of the Senses, and providing Instruction and Amuse- 
ment for Children who are too Young to learn to Read 
and Write. l8*». London. 40 



Grey (Mrs. Wm.) Paper on the Study of Educa- 
tion as a Science. London. 20 

Gross (Magnus). Languages and Popular Edu- 
cation. Tliree Addresses. (The Study of the German 
Language. — The Value of Popular Education. — The 
Study of Languages [with a Table showing the Pedi- 
gree of the Aryan or Indo-European Tribe of Lan- 
guages.]) I2» Paper. New York. 30 

Grosser (W. H.) Illustrative Teaching. 18". 
Flexible cloth. New York. 30 

HAILMAN (W. N.) Outlines. A System of 
Object Teaching prepared for Teachers and Parents. 
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New York. I 00 

Twelve Lectures on the History of Peda- 
gogy, delivered before the Cincinnati Teachers' Asso- 
ciation. 16^. Cincinnati. 75 

Hall (Rev. John.) Familiar Talks to Boys. 12°. 
New York. I 00 

Hamilton (Richard W.) The Institutions of 
Popular Education. Second edition. 12°. London, 
1846. I 25 

Hanna (Sarah R.) Bible History : a Text-book 
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York. I 50 

Hart Qames Morgan). German Universities. A 
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cent Statistical Information, Practical Suggestions, and 
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Systems of Higher Education. 12°. New York, i 75 

Hart Q. S.) In the School-room ; or, Chapters 
in the Philosophy of Education. 12". Phila. i 25 

Mistakes of Educated Men. 18°. Phila- 
delphia. 50 

Harvard Examination Papers. 12". Bos- 
ton. I 50 

Hazen (W. B.) The School and the Army in 
Germany and in France. With a Diary of Siege Life 
at Versailles. 12°. New York. 2 50 

Heberden (W.) On Education. A Dialogue 



after the manner of Cicero's Philosophical Disquisi 
tions. 1 80. London, 1818. 2 2C 

Hecker (John). The Scientific Basis of Educa 
tion, Demonstrated by an Analysis of the Tempera 
ments and of Phrenological Facts in connection with 
Mental Phenomena and the Office of the Holy Spirit 
in the Processes of the Mind, in a Series of Letter? 
to the Department of Public Instruction in the City of 
New York. Second edition. 8°. New York 2 50 

Hiatus: The Void in Modern Education. It? 
Causes and Antidote, by Cutis. 8°. London. 3 00 

Hill (Florence) . Children of the State ; the Train- 
ing of Juvenile Paupers. 16°. London. 2 00 

Hill (Rev. Thomas). The True Order of Studies. 
120. New York. I 25 

History and Progress of Education. 12°. 

New York. I cq 

HlTTELL Qohn S.) A Brief History of Culture. 
12°. New York. I 50 

HOARE (Mrs. Sam'l). Hints on Early Education, 
etc. 120. London. i 00 

HODGINS (J. G.) The School-house : its Architec- 
ture, Arrangements and Disciphne, with Additional 
Papers on Various Subjects. 8°. Toronto, 1858. 2 00 

Special Report on the Ontario Educational 

Exhibit and the Educational Features of the Inter- 
national Exhibition at Philadelphia, 1876. 8". Paper. 
I'oronto. 2 QQ 

HODGSON (W. B.) The Education of Girls, and 
the Employment of Women of the Upper Classes, 
educationally considered. Two lectures. Crown, 
8°. London. i ^q 

HOLBROOK (Alfred). School Management. 12". 
Lebanon. j ^o 

The Normal ; or, Methods of Teaching the 

Common Branches. 12°. New York. i 50 

Hooper (E.) Our Nurseries and School-rooms : 
Bemg remarks on Home Training and Teaching, 
specially for Ladies engaged in Tuition. CiOMn 80. 
London, m^ 



HOOSE (J. H.) Studies in Articulation : a Studj 
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Enghsh Language. i6o. Syracuse. 5c 

• Notes on the Departments of Public In- 
struction in England and Scotland. 16°. Syracuse. 15 

Hope (A. R.) A Book about Boys. 16". Bos- 
ton. 75 

A Book about Dominies. 16°. Boston. 75 

Howe Qulia Ward). Sex and Education. A Re- 
ply to Dr. Clarke's **Sex in Education." 160. Bos 
ton. I 25 

HOYT (John W.) University Progress. 8«. New 
York. 2 oc 

HURST (J. F.) Life and Literature in the Father- 
land. The result of four years' professional residence 
in Germany, and describes fully German Domestic 
and Social Life ; the Schools, Universities, and Gen 
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York. 2 25 

INFANTRY Tactics for Schools. N. Y 75 

JEAN PAUL. Levana; or, the Doctrine of Edu- 
cation. Boston. 2 oc 

Jewell (F. S.) School Government. A Practical 
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Facts, Principles, and their Applications ; with Crit- 
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Schemes of Administration. 12°. New York. I 50 

Jex-Blake (Sophia). A Visit to some American 
Schools and Colleges. 8°. London. i 75 

JOHONNOT (J.) Our School-houses. Containing, 
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About fifty Plans, (4) A simple system of Ventilation, 

(5) Admission of Light and other Sanitary Conditions, 

(6) Arrangement of Grounds, etc., (7) School Furni- 
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Schools, (10) Conduct and Management of Schools. 
Illustrated. 8®. Syracuse. 2 oc 

Jolly (S.) Harmony of Education. 12*'. Lond. 80 

Thoughts on Vocation and Progression of 

the Teacher. I2*». London. 6a 



KAY (J.) The Social Condition and Education 
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Kennedy (H. A.) The Heart and the Mind. 
True Words on Training and Teaching. 12°. Lon- 
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Kennedy (J.) Philosophy of School Discipline. 
160. Syracuse. 21: 

Kiddle (H.). Harrison (T.), and Calkins (N. A.) 
How to Teach. A Manual of Methods for a Grade 
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and School Management. For the use of Teachers. 
120. New York. i 25 

Kingsley (Chas.) Health and Education. 120. 
New York. I >jc 

Kriege (Matilda H.) Friederich Froebel. A Bi- 
ographical Sketch. 120. New York. 50 

Krusi (H.) Pestalozzi : His Life, Work and In- 
fluence. 80. Cincinnati. 2 25 

LANCASTER (Joseph). Improvements in Edu- 
cation, as it respects the Industrial Classes of the 
Community ; containing, among other important par- 
ticulars, an account of the Institution for the Educa- 
tion of One Thousand Poor Children, Borough Road, 
Southwark; and of the New System of Education on 
which it is conducted. 8". London, 1805. 2 00 

Latham (Wm. H.) First Lessons for Deaf Mutes. 
i63. Cincinnati. -20 

Laurie (S. S.) Primary Instruction in relation to 
Education. 12". London. i 50 

Leighton (R. F.) Harvard Examination Papers, 
collected and arranged. 12P. Boston. i 56 

Leitch (James). Practical Educationists and their 
Systems of Teaching, 12°. Glasgow. 240 

Lessing (G. E.) The Education of the Human 
Race. Translated by F. W. Robertson. 180. Lon- 
don. I 00 

Lessons on Objects, as given to Children be- 
tween the Ages of Six and Eight, in a Pestalozzian 



School at Cheam, Surry. From the twenty-second 
London edition. 120. San Francisco. i 75 

Le Vaux (G. V.) The Science and Art of Teach- 
ing. 120. Toronto. I 25 

Library of Education. Selected from the best 
writers of all countries. Vol. I : Some Thoughts 
concerning Education, by John Locke. Vol. 2 : Some 
Thoughts concerning Education, by John Locke ; part 
2, and a Treatise on Education, by John Milton. 
Vol. 3 : The Study of Physiology in Schools, by Hor- 
ace Mann. Vol. 4: Scottish University Addresses, 
by John S. Mill, James A. Froude, and Thos. Car- 
lyle. Vol. 5 : The Bible in the Public Schools, from 
the press, etc. Vol. 6 : The same, part 2. 180. Pa- 
per. Syracuse. Each, 25 

LiLLlENTHAL (M. E.) and Allyn (Robt.) Things 
Taught : Systematic Instruction in Composition and 
Object Lessons. 160. Cincinnati. '25 

LOOMIS (L. C.) Mental and Social Culture, for 
Teachers, Schools, and Families. In Fourteen Chap- 
ters. Adapted for use as a reading book. 12". New 
York. 75 

Lord Qohn). Life of Emma Willard. 12"'. New 
York. 2 00 

Lowe (R.) Primary and Classical Education. 
An Address. 80. Paper. Edinburgh. 50 

MACBRAIR (R. M.) Chapters on National Edu- 
cation. 80. London. 50 

Maclaren (Archibald). A System of Physical 
Education, Theoretical and Practical. With illustra- 
tions. i6». Oxford. 2 25 

Mandeville (Henr)^). Elements of Reading and 
Oratory. 8". New York. i 50 

Mann (Horace). Annual Reports on Education 
from 1S39 to 1848. Crown So. 770 pages. Cloth. 
Boston. 3 00 

Lectures and Annual Reports on Education. 

Crown 80. 584 pages. Cloth. Boston. 3 00 

Thoughts selected from the Writings of 



Horace Mann. 160. 240 pages. Cloth. Bost. I 25 



Mann (Mrs. Horace). The Life of Horace Mann. 
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• Education by Work, according to Froebel's 

Method. Translated from Bertlia Von Marenholz- 
Bulow. 120. Camden. I go 

Mansfield (E. D.) American Education: Its 
Principles and Elements. Dedicated to the Teachers 
of the United States. 120. New York. I 50 

Mark BY (Rev. Thos.) Practical Essays on Edu- 
cation. 12°. London. 2 00 

Martineau (Harriet). Household Education. 
16°. Boston. I 25 

Mathias (G. H. D.) A Tutor's Counsel to his 
Pupils. 120. Philadelphia. I 00 

Maudsley (H.) Sex in Mind and Education. 
160. New York. 25 

Maurice (F. D.) Representation and Education 
of the People. Chapters from Enghsh History. 
Crown 8<*. Paper. London. 75 

Learning and Working. Six Chapters on 

the Foundation of Colleges for Working Men. 80. 
London. 2 50 

Mayhew (Ira). Universal Education : Its Means 
and Ends. 12°. New York. I 75 

Mayo (Miss and Dr.) Practical Remarks on In- 
fant Education. 120. London. 50 

Mayor (J. B.) Guide to the Choice of Classical 
Books. 120. London. i 00 

Menet (J.) Practical Hints on Teaching. Con- 
taining Advice as to Organization, Discipline, Instruc- 
tion, and Practical Management. With plans of 
Schools which have been thoroughly Tested, and are 
now being thoroughly Adopted in various Localities, 
1 20. London. i 25 

Miller (Hugh). My Schools and School-masters. 
1 20. New York. i 50 

More (Hannah). Strictures on the Modem System 
of Female Education ; with a View of the Principles 
and Conduct prevalent among Women of Rank and 
Fortune. 2 vols. 120. London, 1799. 2 25 



MorleyQ.) Struggle for National Education. 8». 

London. I 20 

Morse (E. S.) First Book of Zoology. 12"'. New 

York. I 25 

MuLLER (M.) Public School Education. 12*. 

Boston. I 50 

NASH (Simeon). Crime and the Family. i2'>. 

Cincinnati. I 25 

National Educational Association. Pro- 
ceedings and addresses for 1872, 3, 4, 5, 6 and 7. S". 
Cloth. Each, 2 00 

Newman (Dr. John Henry). Idea of a University ; 
considered in Nine Discourses, Occasional Lectures, 
and Essays. Crown 8". London. 2 80 

New York City. An Account of the Free School 
Society of New York. 80. 1 8 14. Very 7'are. 5 00 

Public Education in its History, Condition 

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Portraits of the Presidents of the Society, by Wm. 
Oland Bourne, A.M. 80. New York. 6 00 

New York State. See Randall (S. S.), Regents' 
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Natural History. This magnificent work, 

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where adopted, is now rare. It consists of 22 vols. 
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)GDEN (J.) The Science of Education and Art 

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Oljn (St.) College Life : Its Theory and Practice. 
120. New York. I 50 

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Orcutt (Hiram). Home and School Training-. 
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Orton (J.) The Liberal Education of Women. 
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Our Children : How to Rear and Train Them. 
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London. I cq 

PAGE (D. P.) Theory and Practice of Teaching. 
1 20. New York. i 50 

Payne Q.) Pestalozzi : The Influence of his Prin- 
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— ' Froebel and the Kindergarten System. 12°. 

Paper. New York. i^ 

« The Science and Art of Education. S**. 

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80. Paper. London. 25 

A Visit to German Schools. Notes of a 



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ples and Practice of Kindergarten and other Schemes 
of Elementary Education. 12°. London. i 80 

Payne (Wm. H.) Chapters on School Supervision. 
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pEABODY (Elizabeth P.) Record of Mr. Alcott's 
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Letters on Early Education. With Me- 
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See Krusi, Payne, Cullen, Barnard, Quick, 



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Phelps (Mrs. L.) The Student ; or, Fireside 
Friend. With an Appendix on Moral and Religious 
Education. I2<'. New York. i 50 

Discipline of Life. 12^. New York, i 75 

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12®. New York. i 50 

Phelps (W. F.) The Teacher's Hand-book for 
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"Philobiblius." History and Progress of Edu- 
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Porter (Noah). Addresses at the Inauguration 
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. Books and Reading ; or. What Books shall 

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History and Traditions. By the author of '* Etoma." 
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PULLEN (P. H.) The Mother's Book ; or, Gram- 
mar of English Parsing; exemplifying Pestalozzi's 
Plan of Awakening the Understanding of Children 
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Numbers. Second edition. 12°. Lond., 1822. i 25 

QUAIN (R.) On some Defects in General Educa- 
tion. Crown 8°. London. i 25 

Quick (Robert Hebert). Essays on Educational 
Reformers. 12°. Cincinnati. 2 oc 

RANDALL (S. S.) A History of the Common 
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York. 3 00 

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Rhode Island History of Public Education, 1636 
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RiCHTER Qean Paul Friedrich). Levana ; or, The 
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RiGG (J. H.) National Education in its Social 
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RiOFREY (A. M. B.) Treatise on Physical Educa- 
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ROBBINS (Eliza). The Guide to Knowledge ; being 

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Answers on Every-day Subjects. i8<». N. Y. i 00 

Roberts (C. R.) National Education ; with Hints 
to People and Rulers. 8". London. 2 40 

Roe (Martha). A Work in Number, for Junior 
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Rogers (Edward). A Guide Book for Parents, 
Teachers, and Scholars, designed as a System of Ethics 
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Rogers (J. E. T.) Education in Oxford: Its 
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Ronneger (Madame). On Certain Moral and 
^Esthetic Deficiencies in the Education of the Present 
Day. Lecture delivered at the College of Preceptors, 
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Root (N. W. Taylor). School Amusements; or. 
How to make the School Interesting, and hints upon 
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Engravings. 120. New York, i 50 



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RoiH (M.) Gymnastic Exercises, according to 
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SANDS (Nathaniel). The Philosophy of Teaching. 
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Culture and Instruction. 18". New York. 75 

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Public Service. 8°. London. 50 

ScoTT (W. R.) The Deaf and Dumb: Their 
Education and Social Position. ,8°. London. 3 00 

Sears (Bamas). Ciceronian : or, the Prussian 
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Children. I2«>. New York. i 75 

Shirreff (Emily). Intellectual Education, and its 
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Smart (J. H.) The Indiana Schools and the Men 
who have Worked in Them. I2<». Cincinnati. I 00 

A Manual of Free Gymnastic and Dumb 

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Man. With an Appendix, containing the Tempera- 
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gland. An Account of the Foundations, Endow- 
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Learning in England. Crown 8<^. London. 2 50 

Steffens (Heinrich). German University Life. 
The Story of My Career as Student and Professor. 
With Personal Reminiscences of Goethe, Schiller, 
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Stetson (C. B.) Technical Education : What it 
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Stone (J.) The Teacher's Examiner. 12". New 
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tion. By the Rev. Wm. Eraser. With Portrait. 
Crown S^. London. 2 00 

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Sweet (J.) Questions for Examinations. An Aid 
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Syntax (Dr.) Three Tours of; in search of (i) 
The Picturesque, (2) Consolation, (3) A Wife. Col- 
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Sypher (J. R.) The Art of Teaching School. 
120. Philadelphia. • I 50 

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London. 2 60 

Taylor (L) Home Education. 8". Lond. 2 00 

Taylor (O. M.) History of Annapolis and the 
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Taylor (S. H.) Method of Classical Study. 12". 
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Dubhn : Its Origin, Progress, and Present Condition. 
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Uncut. 2 50 

Ten Brook (Andrew). American State Univer- 
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American University System. S''. Cincinnati. 3 50 

Testas (M. F.) Virtues and Faults of Childhood. 
From the French by Susan E. Harris. 12°. Bos- 
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Thayer's Lectures to a Young Teacher. 

1 60. New York. 50 

Tho.mas (\V. C.) Symmetrical Education ; or. 
The Importance of Just Proportion in Mind and Body. 
Crown 8^. London. I 00 

FhomPSON (D'Arcy W.) Day Dreams of a School- 
master. 12^. London. 2 50 

• Wayside Thoughts on Education. 12". 

Edinburgli. 2 40 

Thomson (E.) Educational Essays. 12". New 
York. I 50 



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Thring (E.) Education and School. 120. Lon- 
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Times (J.) School Days of Eminent Men. 12°. 
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TODHUNTER (I.) The Condict of Studies, and 
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Twining (T.) Technical Training: Being a Sug- 
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Science among the People. 8°. London. 4 50 

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portant Educational Subjects. Carefully compiled, 
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120. New York. I 00 

Warren (S. E.) Notes on Polytechnic or Scien- 
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Posidon, Aims, and Wants. 8^. Paper. N. Y. 40 

Watson's (J. M.) Handbook of Gymnastics. 
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Manual of Calisthenics. A Complete Course 

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York. I 25 

Welch (A. S.) Object Lessons. Prepared for 
Teachers of Primary Schools and Primary Classes. 
160, New York. i 00 

Welch (F. G.) Moral, Intellectual, and Physical 
Culture; or, The Philosophy of True Living. 120. 
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Wells (VV. H.) A Graded Course of Instruction 
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New York. i 25 

Western Literary Institute and College of Pro- 
fessional Teachers. Transactions of Fourth Annual 
Meeting. S^. Cincinnati, 1835. 2 00 

Whewell (Wm.) Of a Liberal Education in Gen- 
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Studies of the University of Cambridge. 8°. Boards. 
London. 2 00 

On the Principles of English University 

Education. 12". London, 1838. I 25 

Influence of the History of Science upon In- 



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White (R. G.) Life and Genius of Shakspere. 
120. Boston. 2 50 

Whitcomb (Ida P.) A Summary of History. 
120. New York. 50 

WiCKERSHAM (J. P.) Methods of Instruction ; or. 
That Part of the Philosophy of Education, which 
Treats of the Nature of the Several Branches of 
Knowledge, and the Method of Teaching Them. I2». 
Philadelphia. I 75 

School Economy. A Treatise on the Prep- 
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Authorities of Schools. 12°. Philadelphia. I 50 

WiLLARD (Emma). The Life of, by John Lord. 
120. New York. 2 00 

WiLLSON (M.) Manual of Information and Sug- 
gestions for Object Lessons, in a Course of Element- 
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and Family Charts, and other aids in Teaching. 120. 
New York. I 50 

WiLLiN (J.) The Education of the People ; with 
J. P. Nichols's Preliminary Dissertation. 120. Glas- 
gow. 15^ 

Wordsworth (C.) Social Life at the English 

Universities in the Eighteenth Century. 12°. Lon- 

don. 6 00 

Work's New Education according to Froebel's 

Method, by Bertha Von Marenholtz-Bulow. Trans- 



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Prof. Leopold Noa. i6o. 1876. 50 

Y'ONGE (Miss). Landmarks of Ancient History. 
12". New York. I 00 

• Landmarksof Mediaeval History. 12°. New 

York. I 25 

■ Landmarks of Modern History. 12'^. New 

York. I 50 

YOUMANS (E. L.) The Culture Demanded by 
Modern Life : A Series of Addresses and Arguments 
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12°. New York. 2 00 

YoUMANS (Eliza A.) First Book of Botany. De- 
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120. New York. i 25 

Second Book of Botany. 12". N. Y. i 50 

SCHOOL REPORTS 

Of all leading States and Cities for many years past 
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KINDERGARTEN. 

BORSCHITZKY (J. F.) Kindergarten Lieder, with 
German and English words. Containing the 32 Songs 
in Ronge's Guide. Arranged with an accompaniment 
of a second voice and piano-forte guidance. New 
York. 3 50 

■ Thirty-two Songs from Ronge's Kinder- 
garten Guide, with words in English and German. 
New York. I 75 

New Kindergarten Songs. New York. 50 



CURRIE (James). The Principles and Practice of 
Early and Infant School Education, with an Appendix 
of Infant School Hymns and Songs with appropriate 
Melodies. 12**. London. 2 00 

DOUAI (Adoll). The Kindergarten. A Manual 
for the Introduction of Froebel's System of Primary 
Education into Public Schools, and for the Use of 
Mothers and Private Teachers. With 16 plates. 
Fourth edition. 120. New York. I 00 



Froebel (F.) The Founder of the Kindergarten 
System. A Biographical Sketch by Matilda H. Kriege, 
with portrait. Cloth. New York. 5a 

. Reminiscences, by B. Von Marenholz-Bu- 

low. 12". Boston. I 50 

■ The Mother's Book of Song. Two-part 

Songs for little Singers, on the Kindergarten System. 
The music composed by Lady Baker ; edited by G. A. 
Macfarran. 160. New York. 75 

Froebel (Karl). Elements of Designing on the 
Developing System, for Elementary School Classes, 
and for Families. 4 parts. Leipsic. 

Each, paper, $0.35; cloth 50 

Hailman (W. N.) Kindergarten Culture in the 
Family and Kindergarten. A Complete Sketch of 
Froebel's System of Early Education, adapted to 
American Institutions. For the use of Mothers and 
Teachers. Illustrated. 16**. Cincinnati. 75 

Hoffmann (H.) Kindergarten Toys, and how to 
use Them. A Practical Explanation of the First Six 
Gifts of Froebel's Kindergarten. Illustrated. Paper. 
New York. 20 

Hyde (Anna M.) A Ladder to Learning for Little 
Climbers. Showing how Play and Study may be 
Combined. Prepared for the Use of Kindergartens, 
Infants, Primary, and Parish Schools. 18°. Phila- 
delphia. 50 

Kraus-Boelte (Maria) and John Kraus. The 
Kindergarten Guide. An Illustrated Hand-book, de- 
signed for the Self-instruction of Kindergartners, 
Mothers, and Nurses. 80. New York. No, I, ist 
and 2d Gifts, $0.65; II, 3d-6th, $1.00; III, 7th 
Gift, 80 

Kriege (A. L.) Rhymes and Tales for the Kin- 
dergarten and Nursery. Collected and revised. I2<'. 
New York. Paper, $0.50; cloth I 00 

Kriege (Matilda H.) The Child : Its Nature and 
Relations. An Elucidation of Froebel's Principles of 
Education. Second edition. 12°. New York, i 00 

Little (Ella). Kindergarten Spelling-book. Part 
first. 16". Boston. 25 



Mann (Mrs. H.) and Peabody (E. O.) Moral 
Culture of Infancy and Kindergarten Guide, with 
music for the Plays. 12^ New York. I 25 

No A (Henrietta). Plays for the Kindergarten ; 
music by C. J. Richter. (The Text of the 19 Plays is 
in both German and English.) 18°. Paper. New 
York. 30 

Payne Qoseph). Froebel and the Kindergarten 
System of Elementary Education. Paper. N. Y. 15 

Peabody (Elizabeth P.) Lectures on the Nursery 
and Kindergartner. No. I. Education of the Kin- 
dergartner. 120. Paper. Pittsburg. 25 

Ronge (Johannes and Bertha). A Practical Guide 
to the English Kindergarten, for the use of Mothers, 
Governesses, and Infant Teachers ; being an Exposi- 
tion of Froebel's System of Infant Training, accompa- 
nied with a great variety of Instructive and Amusing 
Games, and Industrial and Gymnastic Exercises. 
Willi numerous Songs set to Music, and arranged for 
the Exercises. With 71 lithographic plates. New 
York. 2 10 

Wiebe (Ed.) The Paradise of Childhood. A 
Manual for Self-instruction in Friedrich Froebel's Ed- 
ucational Principles, and a Practical Guide to Kinder- 
gartners. With 74 plates of Illustrations. In four 
parts. 4°. Springfield, Mass. Paper, $2.50; cl. 3 GO 

See also Works on "Objects." 

NATURAL HISTORY OF THE STATE OF 
NEW YORK. 

This magnificent work was issued by this State at an 
expense exceeding $500,000, and gave to the world the 
accepted nomenclature of geological formations. Twen- 
ty-two volumes have been issued : the first in 1842, the 
last in 1870. Complete sets are now scarce and valuable, 
but we have for several years purchased all copies offered 
for sale, and have now on hand several complete sets, 
and a great many single volumes. The prices of the 
different volumes vary with their scarcity and condition. 
The Mineralogy we can furnish at $3.00. The Orni- 



thology is scarce at $15.00. Complete sets are worth 
from $80.00 to $120.00, according to the condition and 
coloring of the plates. We shall be glad to correspond 
with persons desiring either to buy or to sell. 

Full sets have been furnished to Principal Veeder, of 
Ives Seminary, Antwerp; Principal Dolph, of Port 
Jervis High School; J. Dorman Steele, Ph.D., of El- 
mira, and several others, and we have filled incomplete 
sets in every part of the State. 

SUBJECTS. 

Zoology. — Vol. i. Historical introduction to th 
Series, by Hon. William H. Seward, and Zoology of 
New York, or The New York Fauna. Mammalia. 
Text and 33 full page Plates. By James E. De Kay. 
Issued in 1842. — Vol. 2. Birds (Ornithology). Text 
and 308 Colored Figures. By James E De Kay. 1844. 
— Vol, 3. Reptiles, Fishes and Amphibia. Text. By 
James E. De Kay.' 1842. — Vol. 4. Reptiles, Fishes 
and Amphibia. 102 full page Plates. By James E. De 
Kay. 1842. — Vol. 5. Mollusca and Crustacea. Text 
with 53 full page Colored Plates. By James E. De Kay. 
1843 and 1844. 

Botany.— Vol. 6. Flora of the State of New York 
Text and 72 full page Plates. By John Torrey, M.D., 
F.L.S. 1843. —Vol. 7. Flora of the State of New 
York. Text and 89 full page Plates. By John Toirey, 
M.D., F.L.S. 1843. 

Mineralogy. — Vol. 8. Mineralogy of New York 
(in one vol.) By Lewis C. Beck, M.D., Prof, of Chem- 
istry and Natural History. Profuse Illustrations and 8 
full page Plates. 1842. 

Geology. — Vol. 9. Geology of New York, compris- 
ing the Geology of Washington, Saratoga, Schenectady, 
Schoharie and Delaware counties, and all territory with- 
in the State south and east of these counties, with 9 fold- 
ed and 37 full page Plates, colored. By William W. 
Mather, -Prof of Nat. Hist. 1843.— Vol.- 10. Second 
Geological District, embracing St. Lawrence, Frankhn., 
Clinton, Essex, Warren, Hamilton and Jefferson coun- 
ties, with 10 folded and 7 full page maps, colored. By 
Ebenezer Emmons, Prof, of Nat. Hist. 1842.— Vol 



rt. Third Geological District, embracing Monrgom- 
er^, Fulton, Otsego, Herkimer, Oneida, Lewis, Oswe- 
go, Madison, Onondaga, Cayuga, Cortland, Chenango, 
Broome, Tioga and the eastern half of Tompkins coun- 
ties, with many illustrations. By Lardner Vanuxem. 
1842. — Vol. 12. Fourth Geological District, embracing 
Wayne, Monroe, Orleans, Niagara, Seneca, Ontario, 
Yates, Livingston, Genesee, Erie, Chemung, Steuben, 
Allegany, Cattaraugus, Chautauqua and the western part 
of Tompkins counties, with 15 folded Plates, colored, 
ind 80 full page Plates. By James Hall. 1843. 

Agriculture. — Vol. 13. Agriculture of New York, 
jlassification, etc., of Soils and Rocks. 8 folded, 13 full 
page Plates, colored. By Ebenezer Emmons, M.D. 
1846. — Vol. 14. Agriculture of New York, analysis of 
Soils, Plants, Cereals, etc. 43 full page Plates, colored. 
By Ebenezer Emmons, M.D. 1849. — Vol. 15. Agri- 
culture of New York, Fruits of the State. Many Illus- 
trations. By Ebenezer Emmons, M.D. 1851. — Vol. 
16. Agriculture of Ne\v York, Fruits (vol. HI on title 
page). 99 full page Colored Plates. By Ebenezer Em- 
mons, M.D. 1851. — Vol. 17. Agriculture of New 
York, Insects injurious to Agriculture. Over looo Col- 
ored Figures. By Ebenezer Emmons, M.D. 1854. 

pAi.^toNTOLOGY. — Vol. i8. Palaeontology of New 
York, Organic remains of the Lower Silurian. 97 full 
page and folded Plates. By James Hall. 1847. — Vol. 

19. Organic remains of the Middle Silurian. 98 full 
page and folded Plates. By James Hall. 1853. — Vol. 

20. Organic remains of the Lower Helderberg Group 
and Oriskany Sandstone. By James Hall. 1859. — 
Vol. 21. 150 full page Plates to the same. By James 
Hall. 1862. — Vol. 22. Fossil Brachiopoda of the Upper 
Helderberg, Hamilton, Portage and Chemung Groups, 
etc 75 full page Plates. By James Hall. Issued 
1870. 

REGENTS' REPORTS ON THE MUSEUM OF 
NATURAL HISTORY. 

These Reports form Annual Supplements to the Nat- 
ural History' of the State of New York, and are even 
more rare and in some cases more valuable than the vol 



umes of Natural History themselves. We have on« 
complete set, except the first two volumes, and many 
duplicates, including the Report of the Legislative Com 
mittee upon the history and cost of the Natural History 
of New York. Prices furnished on application. 

Index to the Reports. 

No. Ill, 1850. Catalogue^; of Quadrupeds, Reptiles 
and Amphibians, Minerals and Fossils, Historical and 
Antiquarian Collection. Reports — on Indian Collection, 
by Lewis H. Morgan, with cuts and beautifully colored full 
page plates ; on ancient Remains of Art in Jefferson and 
St. Lawrence counties, by Franklin B. Hough, with 5 
full page illustrations ; on the Mineralogy of New York, 
by Lewis H. Beck, with cuts. References to various 
Essays and Writings on the Natural History of New 
York. Index to the Volumes in the State Cabinet of 
Natural History. Description of New Species of Fos- 
sils from the Trenton Limestone, by James Hall, with 3 
full page and i folded illustrations. Pp. 183. 

No. IV, 1 85 1. Catalogues of Quadrupeds, Birds, 
Reptiles, Amphibians, Insects, Botanical Specimens, 
Minerals and Fossils, with cuts, Historical Collection. 
Ancient Remains, continued from No. Ill, with cuts 
and 5 full page illustrations, etc. Pp. 146. 

No. V, 1852. The usual annual catalogues of addi- 
tions. Description of the means employed by E. Mer- 
riam to remove the rocks of Hurlgate, etc. Pp. 66. 
Appendix. Report on the Fabrics, Inventions, Im- 
plements and Utensils of the Iroquois, by Lewis H. 
Morgan, with many cuts and 20 full page colored illustra- 
tions. Pp. 66. 

No. VI, 1853. The usual annual catalogues. Pp. 35. 

No. VII, 1854. The usual annual catalogues. Com- 
munication from Prof. Geo. H. Cook, oin Salt and Salt 
Water, On the Serpents of New York, by Spencer F. 
Baird, with 2 full page plates. Pp. 127. 

No. VIII, 1855. The usual catalogues, with folded 
plate of Trilobite. Also, catalogue of the Fishes of the 
State, by James E. De Kay. Pp. 69. 

No. IX, 1856. The usual catalogues. Pp. 48. 



No. X, 1857. Addresses delivered at the Inaugur* 
tion of the State Geological Hall. The usual catalogues, 
with cuts of Fossils. Pp. 190. 

No. XI, 1858. The usual catalogues. Pp. 44. 

No. XII, 1859. Contributions to the Palaeontology 
of New York, 1855-8, by James Hall. The usual cata- 
logues. Pp. III. 

No. XIII, i860. The usual catalogues. Catalogue 
of the Mazatlan Mollusca. Ancient Monuments of 
Western New York, by T. Apoleon Cheney, with map 
and 27 full page plates. Contributions to Palaeontology, 
1858-9, by James Hall. Pp. 128. 

No. XIV, 1861. The usual catalogues. Guide to 
the Geology of New York, by Ledyard Lincklaen, with 
cuts and 19 full page plates. Contributions, 1859-60, 
by James Hall. Pp. iio. 

No. XV, 1862. The usual catalogues. Contributions 
as to the Upper Helderberg, Hamilton and Chemung 
Groups, by James Hall, with ii full page plates. Pp. 
181. 

No. XVI, 1863. The usual catalogues. Radical 
Words of the Mohawk Language, by Rev. James 
Bruyas, S.J. Pp. 123. Appendix D (separate volume). 
Contributions to Palaeontology, 1861-2, by James Hall, 
with cuts and 15 full page illustrations. Pp. 226. 

No. XVII, 1864. The usual catalogues. Prelimi- 
nary List of Plants of Buffalo and its Vicinity, by Geo. 
W. Clinton. Meteorological Observations. Contribu- 
tions to Palaeontology, by James Hall. Pp. 60. 

No. XVIII, 1865. The usual catalogues. Descrip- 
tion of the Wadsworth Gallery of Casts of Fossil Ani- 
mals, by Henry A. Ward, with profuse illustrations. 
Catalogue of Plants found in Oneida county and Vicinity, 
by John A. Paine. Catalogue of Mosses, by Charles 
H. Peck. Facts and Observations touching the Flora 
of the State of New York. Meteorological Observations. 
Table of the Variation of the Needle. Pp. 232. Con- 
tributions to Palaeontology, by James Hall, are indexed, 
Dut were printed in the Twentieth Report. 

No. XIX, 1866. Special Report on increasing the 
Cabinet of Natural History. The usual catalogues. 



Catalogue of Mosses and Observations on Flora of the 
State continued. Contributions, by James Hall. Pp. 8o. 

No. XX, 1867. The usual catalogues. Catalogue of 
Books. Local Climatology. Metorological Observa- 
tions. Local Climatology, by Prof. W. D. Wilson. 
Observations on the Atrypa, with cuts. Contributions 
to Palaeontology, by James Hall, including the study of 
Graptolites, etc., profusely illustrated, 23 full page illus- 
trations. Pp. 410. 

No. XXI, 1868. The usual catalogues. The Stone 
•and Bone Implements of the Arickarees, by Lewis H. 
Morgan, with 6 full page plates. The Mineralogy of 
the Laurentian Limestonesof North America, byT. Sterry 
Hunt. Notes and Observations on the Cohoes* Masto- 
don, by James Hall, with 7 folded plates. General In- 
dex to Reports I-XX, exclusive of the Geological and 
Palaeontological Papers. Pp. 190. 

No. XXII, 1869. The usual catalogues. Partial list 
of Shells found near Troy, by Truman H. Aldrich. 
Reports on Meteorology and Magnetic Variations. Pp. 

"3- 

No. XXIII, 1870. The usual catalogues. Report of 
the Botanist, with 6 full page colored illustrations. En- 
tomological Contributions, by J. A. Lintner, with 2 full 
page illustrations. On Cucullia, by A. Speyer, M.D. 
Notes on Brachiopoda, with 6 full page illustrations, and 
Reply to a Note on a Question of Priority, by James 
Hall. Pp. 252. 

No. XXIV, 1871. The usual catalogues. Report of 
the Botanist, with 4 full page colored plates. Entomo- 
logical Contributions, continued. Ascent of Mt. Sew- 
ard, and its Barometrical Measurement, by Verplanck 
Colvin, with one full page illustration. Description of 
Fossils from Louisville, Ky., and Remarks on Peculiar 
Impressions in Sandstone of the Chemung Group, by 
Tames Hall and R. P. Whitfield. Descriptions of Cri- 
iioidea, and of new Fossils from Cincinnati, by Jame.s 
Hall, with 4 full page plates. Pp. 232. 

No. XXV, 1872. The usual catalogues. Report of 
Ihe Botanist, with two full page illustrations. Pp. 123. 

No. XXVI, 1873. The usual catalogues. List of 



Iron Ores in the Economic Collection. Record of Bor« 
ings of Gardner Oil Well. Report of the Botanist. 
Fossils in the Lower Helderberg Group, by James Hall. 
Entomological Contributions, No. 3, with cuts. Pp. 192. 
No. XXVII, 1874. The usual catalogues. List of 
Land and Fresh Water Shells, by T. H. Aldrich. Re- 
port of the Botanist, with 2 full page illustrations. Tha 
Niagara and Lower Helderberg Groups, and New Spe- 
cies of Gomatitidae, by James Hall, with 5 full page il. 
lustrations. Entomological Contributions, No. 4. Pp. 
U8. I 



THE 



IM Bietin FnlilicatioM. 



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3. The School Bulletin Year-Book.— Vol. I., 1878. A complete 
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4. Common School Law for Common School Teachers.— The stand- 
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11. Beebe's First Steps among Figures.— The simplest and clearest 
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